---
_id: '53539'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>The infinite Brownian loop on a
    Riemannian manifold is the limit in distribution of the Brownian bridge of length
    <jats:italic>T</jats:italic> around a fixed origin when <jats:inline-formula><jats:alternatives><jats:tex-math>$$T
    \\rightarrow +\\infty $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \               <mml:mrow>\r\n                  <mml:mi>T</mml:mi>\r\n                  <mml:mo>→</mml:mo>\r\n
    \                 <mml:mo>+</mml:mo>\r\n                  <mml:mi>∞</mml:mi>\r\n
    \               </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>.
    The aim of this note is to study its long-time asymptotics on Riemannian symmetric
    spaces <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic> of noncompact
    type and of general rank. This amounts to the behavior of solutions to the heat
    equation subject to the Doob transform induced by the ground spherical function.
    Unlike the standard Brownian motion, we observe in this case phenomena which are
    similar to the Euclidean setting, namely <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:msup>\r\n
    \                 <mml:mi>L</mml:mi>\r\n                  <mml:mn>1</mml:mn>\r\n
    \               </mml:msup>\r\n              </mml:math></jats:alternatives></jats:inline-formula>
    asymptotic convergence without requiring bi-<jats:italic>K</jats:italic>-invariance
    for initial data, and strong <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{\\infty
    }$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \               <mml:msup>\r\n                  <mml:mi>L</mml:mi>\r\n                  <mml:mi>∞</mml:mi>\r\n
    \               </mml:msup>\r\n              </mml:math></jats:alternatives></jats:inline-formula>
    convergence.</jats:p>"
author:
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
citation:
  ama: Papageorgiou E. Asymptotics for the infinite Brownian loop on noncompact symmetric
    spaces. <i>Journal of Elliptic and Parabolic Equations</i>. Published online 2023.
    doi:<a href="https://doi.org/10.1007/s41808-023-00250-8">10.1007/s41808-023-00250-8</a>
  apa: Papageorgiou, E. (2023). Asymptotics for the infinite Brownian loop on noncompact
    symmetric spaces. <i>Journal of Elliptic and Parabolic Equations</i>. <a href="https://doi.org/10.1007/s41808-023-00250-8">https://doi.org/10.1007/s41808-023-00250-8</a>
  bibtex: '@article{Papageorgiou_2023, title={Asymptotics for the infinite Brownian
    loop on noncompact symmetric spaces}, DOI={<a href="https://doi.org/10.1007/s41808-023-00250-8">10.1007/s41808-023-00250-8</a>},
    journal={Journal of Elliptic and Parabolic Equations}, publisher={Springer Science
    and Business Media LLC}, author={Papageorgiou, Efthymia}, year={2023} }'
  chicago: Papageorgiou, Efthymia. “Asymptotics for the Infinite Brownian Loop on
    Noncompact Symmetric Spaces.” <i>Journal of Elliptic and Parabolic Equations</i>,
    2023. <a href="https://doi.org/10.1007/s41808-023-00250-8">https://doi.org/10.1007/s41808-023-00250-8</a>.
  ieee: 'E. Papageorgiou, “Asymptotics for the infinite Brownian loop on noncompact
    symmetric spaces,” <i>Journal of Elliptic and Parabolic Equations</i>, 2023, doi:
    <a href="https://doi.org/10.1007/s41808-023-00250-8">10.1007/s41808-023-00250-8</a>.'
  mla: Papageorgiou, Efthymia. “Asymptotics for the Infinite Brownian Loop on Noncompact
    Symmetric Spaces.” <i>Journal of Elliptic and Parabolic Equations</i>, Springer
    Science and Business Media LLC, 2023, doi:<a href="https://doi.org/10.1007/s41808-023-00250-8">10.1007/s41808-023-00250-8</a>.
  short: E. Papageorgiou, Journal of Elliptic and Parabolic Equations (2023).
date_created: 2024-04-17T13:16:39Z
date_updated: 2026-07-03T12:36:17Z
department:
- _id: '555'
doi: 10.1007/s41808-023-00250-8
keyword:
- Applied Mathematics
- Numerical Analysis
- Analysis
language:
- iso: eng
publication: Journal of Elliptic and Parabolic Equations
publication_identifier:
  issn:
  - 2296-9020
  - 2296-9039
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Asymptotics for the infinite Brownian loop on noncompact symmetric spaces
type: journal_article
user_id: '100325'
year: '2023'
...
---
_id: '16296'
abstract:
- lang: eng
  text: "Multiobjective optimization plays an increasingly important role in modern\r\napplications,
    where several objectives are often of equal importance. The task\r\nin multiobjective
    optimization and multiobjective optimal control is therefore\r\nto compute the
    set of optimal compromises (the Pareto set) between the\r\nconflicting objectives.
    Since the Pareto set generally consists of an infinite\r\nnumber of solutions,
    the computational effort can quickly become challenging\r\nwhich is particularly
    problematic when the objectives are costly to evaluate as\r\nis the case for models
    governed by partial differential equations (PDEs). To\r\ndecrease the numerical
    effort to an affordable amount, surrogate models can be\r\nused to replace the
    expensive PDE evaluations. Existing multiobjective\r\noptimization methods using
    model reduction are limited either to low parameter\r\ndimensions or to few (ideally
    two) objectives. In this article, we present a\r\ncombination of the reduced basis
    model reduction method with a continuation\r\napproach using inexact gradients.
    The resulting approach can handle an\r\narbitrary number of objectives while yielding
    a significant reduction in\r\ncomputing time."
author:
- first_name: Stefan
  full_name: Banholzer, Stefan
  last_name: Banholzer
- first_name: Bennet
  full_name: Gebken, Bennet
  id: '32643'
  last_name: Gebken
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Stefan
  full_name: Volkwein, Stefan
  last_name: Volkwein
citation:
  ama: 'Banholzer S, Gebken B, Dellnitz M, Peitz S, Volkwein S. ROM-Based Multiobjective
    Optimization of Elliptic PDEs via Numerical Continuation. In: Michael H, Roland
    H, Christian K, Michael U, Stefan U, eds. <i>Non-Smooth and Complementarity-Based
    Distributed Parameter Systems</i>. Springer; 2022:43-76. doi:<a href="https://doi.org/10.1007/978-3-030-79393-7_3">10.1007/978-3-030-79393-7_3</a>'
  apa: Banholzer, S., Gebken, B., Dellnitz, M., Peitz, S., &#38; Volkwein, S. (2022).
    ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.
    In H. Michael, H. Roland, K. Christian, U. Michael, &#38; U. Stefan (Eds.), <i>Non-Smooth
    and Complementarity-Based Distributed Parameter Systems</i> (pp. 43–76). Springer.
    <a href="https://doi.org/10.1007/978-3-030-79393-7_3">https://doi.org/10.1007/978-3-030-79393-7_3</a>
  bibtex: '@inbook{Banholzer_Gebken_Dellnitz_Peitz_Volkwein_2022, place={Cham}, title={ROM-Based
    Multiobjective Optimization of Elliptic PDEs via Numerical Continuation}, DOI={<a
    href="https://doi.org/10.1007/978-3-030-79393-7_3">10.1007/978-3-030-79393-7_3</a>},
    booktitle={Non-Smooth and Complementarity-Based Distributed Parameter Systems},
    publisher={Springer}, author={Banholzer, Stefan and Gebken, Bennet and Dellnitz,
    Michael and Peitz, Sebastian and Volkwein, Stefan}, editor={Michael, Hintermüller
    and Roland, Herzog and Christian, Kanzow and Michael, Ulbrich and Stefan, Ulbrich},
    year={2022}, pages={43–76} }'
  chicago: 'Banholzer, Stefan, Bennet Gebken, Michael Dellnitz, Sebastian Peitz, and
    Stefan Volkwein. “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical
    Continuation.” In <i>Non-Smooth and Complementarity-Based Distributed Parameter
    Systems</i>, edited by Hintermüller Michael, Herzog Roland, Kanzow Christian,
    Ulbrich Michael, and Ulbrich Stefan, 43–76. Cham: Springer, 2022. <a href="https://doi.org/10.1007/978-3-030-79393-7_3">https://doi.org/10.1007/978-3-030-79393-7_3</a>.'
  ieee: 'S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, and S. Volkwein, “ROM-Based
    Multiobjective Optimization of Elliptic PDEs via Numerical Continuation,” in <i>Non-Smooth
    and Complementarity-Based Distributed Parameter Systems</i>, H. Michael, H. Roland,
    K. Christian, U. Michael, and U. Stefan, Eds. Cham: Springer, 2022, pp. 43–76.'
  mla: Banholzer, Stefan, et al. “ROM-Based Multiobjective Optimization of Elliptic
    PDEs via Numerical Continuation.” <i>Non-Smooth and Complementarity-Based Distributed
    Parameter Systems</i>, edited by Hintermüller Michael et al., Springer, 2022,
    pp. 43–76, doi:<a href="https://doi.org/10.1007/978-3-030-79393-7_3">10.1007/978-3-030-79393-7_3</a>.
  short: 'S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, S. Volkwein, in: H. Michael,
    H. Roland, K. Christian, U. Michael, U. Stefan (Eds.), Non-Smooth and Complementarity-Based
    Distributed Parameter Systems, Springer, Cham, 2022, pp. 43–76.'
date_created: 2020-03-13T12:45:31Z
date_updated: 2022-03-14T13:04:51Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/978-3-030-79393-7_3
editor:
- first_name: Hintermüller
  full_name: Michael, Hintermüller
  last_name: Michael
- first_name: Herzog
  full_name: Roland, Herzog
  last_name: Roland
- first_name: Kanzow
  full_name: Christian, Kanzow
  last_name: Christian
- first_name: Ulbrich
  full_name: Michael, Ulbrich
  last_name: Michael
- first_name: Ulbrich
  full_name: Stefan, Ulbrich
  last_name: Stefan
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/pdf/1906.09075.pdf
oa: '1'
page: 43-76
place: Cham
publication: Non-Smooth and Complementarity-Based Distributed Parameter Systems
publication_identifier:
  isbn:
  - 978-3-030-79392-0
publisher: Springer
status: public
title: ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation
type: book_chapter
user_id: '47427'
year: '2022'
...
---
_id: '30294'
abstract:
- lang: eng
  text: With the ever increasing capabilities of sensors and controllers, autonomous
    driving is quickly becoming a reality. This disruptive change in the automotive
    industry poses major challenges for manufacturers as well as suppliers as entirely
    new design and testing strategies have to be developed to remain competitive.
    Most importantly, the complexity of autonomously driving vehicles in a complex,
    uncertain, and safety-critical environment requires new testing procedures to
    cover the almost infinite range of potential scenarios.
author:
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
- first_name: Sebastian
  full_name: Bannenberg, Sebastian
  last_name: Bannenberg
citation:
  ama: 'Peitz S, Dellnitz M, Bannenberg S. Efficient Virtual Design and Testing of
    Autonomous Vehicles. In: Bock HG, Küfer K-H, Maas P, Milde A, Schulz V, eds. <i>German
    Success Stories in Industrial Mathematics</i>. Vol 35. Mathematics in Industry.
    Springer International Publishing; 2022. doi:<a href="https://doi.org/10.1007/978-3-030-81455-7_23">10.1007/978-3-030-81455-7_23</a>'
  apa: Peitz, S., Dellnitz, M., &#38; Bannenberg, S. (2022). Efficient Virtual Design
    and Testing of Autonomous Vehicles. In H. G. Bock, K.-H. Küfer, P. Maas, A. Milde,
    &#38; V. Schulz (Eds.), <i>German Success Stories in Industrial Mathematics</i>
    (Vol. 35). Springer International Publishing. <a href="https://doi.org/10.1007/978-3-030-81455-7_23">https://doi.org/10.1007/978-3-030-81455-7_23</a>
  bibtex: '@inbook{Peitz_Dellnitz_Bannenberg_2022, place={Cham}, series={Mathematics
    in Industry}, title={Efficient Virtual Design and Testing of Autonomous Vehicles},
    volume={35}, DOI={<a href="https://doi.org/10.1007/978-3-030-81455-7_23">10.1007/978-3-030-81455-7_23</a>},
    booktitle={German Success Stories in Industrial Mathematics}, publisher={Springer
    International Publishing}, author={Peitz, Sebastian and Dellnitz, Michael and
    Bannenberg, Sebastian}, editor={Bock, H. G. and Küfer, K.-H. and Maas, P. and
    Milde, A. and Schulz, V.}, year={2022}, collection={Mathematics in Industry} }'
  chicago: 'Peitz, Sebastian, Michael Dellnitz, and Sebastian Bannenberg. “Efficient
    Virtual Design and Testing of Autonomous Vehicles.” In <i>German Success Stories
    in Industrial Mathematics</i>, edited by H. G. Bock, K.-H. Küfer, P. Maas, A.
    Milde, and V. Schulz, Vol. 35. Mathematics in Industry. Cham: Springer International
    Publishing, 2022. <a href="https://doi.org/10.1007/978-3-030-81455-7_23">https://doi.org/10.1007/978-3-030-81455-7_23</a>.'
  ieee: 'S. Peitz, M. Dellnitz, and S. Bannenberg, “Efficient Virtual Design and Testing
    of Autonomous Vehicles,” in <i>German Success Stories in Industrial Mathematics</i>,
    vol. 35, H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, and V. Schulz, Eds. Cham:
    Springer International Publishing, 2022.'
  mla: Peitz, Sebastian, et al. “Efficient Virtual Design and Testing of Autonomous
    Vehicles.” <i>German Success Stories in Industrial Mathematics</i>, edited by
    H. G. Bock et al., vol. 35, Springer International Publishing, 2022, doi:<a href="https://doi.org/10.1007/978-3-030-81455-7_23">10.1007/978-3-030-81455-7_23</a>.
  short: 'S. Peitz, M. Dellnitz, S. Bannenberg, in: H.G. Bock, K.-H. Küfer, P. Maas,
    A. Milde, V. Schulz (Eds.), German Success Stories in Industrial Mathematics,
    Springer International Publishing, Cham, 2022.'
date_created: 2022-03-14T07:32:41Z
date_updated: 2022-03-14T07:42:01Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/978-3-030-81455-7_23
editor:
- first_name: H. G.
  full_name: Bock, H. G.
  last_name: Bock
- first_name: K.-H.
  full_name: Küfer, K.-H.
  last_name: Küfer
- first_name: P.
  full_name: Maas, P.
  last_name: Maas
- first_name: A.
  full_name: Milde, A.
  last_name: Milde
- first_name: V.
  full_name: Schulz, V.
  last_name: Schulz
intvolume: '        35'
language:
- iso: eng
place: Cham
publication: German Success Stories in Industrial Mathematics
publication_identifier:
  isbn:
  - '9783030814540'
  - '9783030814557'
  issn:
  - 1612-3956
  - 2198-3283
publication_status: published
publisher: Springer International Publishing
series_title: Mathematics in Industry
status: public
title: Efficient Virtual Design and Testing of Autonomous Vehicles
type: book_chapter
user_id: '47427'
volume: 35
year: '2022'
...
---
_id: '30490'
author:
- first_name: Jacky
  full_name: Cresson, Jacky
  last_name: Cresson
- first_name: Fernando
  full_name: Jiménez, Fernando
  last_name: Jiménez
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
citation:
  ama: Cresson J, Jiménez F, Ober-Blöbaum S. Continuous and discrete Noether’s fractional
    conserved quantities for restricted calculus of variations. <i>AIMS</i>. 2022;14(1):57-89.
  apa: Cresson, J., Jiménez, F., &#38; Ober-Blöbaum, S. (2022). Continuous and discrete
    Noether’s fractional conserved quantities for restricted calculus of variations.
    <i>AIMS</i>, <i>14(1)</i>, 57–89.
  bibtex: '@article{Cresson_Jiménez_Ober-Blöbaum_2022, title={Continuous and discrete
    Noether’s fractional conserved quantities for restricted calculus of variations},
    volume={14(1)}, journal={AIMS}, author={Cresson, Jacky and Jiménez, Fernando and
    Ober-Blöbaum, Sina}, year={2022}, pages={57–89} }'
  chicago: 'Cresson, Jacky, Fernando Jiménez, and Sina Ober-Blöbaum. “Continuous and
    Discrete Noether’s Fractional Conserved Quantities for Restricted Calculus of
    Variations.” <i>AIMS</i> 14(1) (2022): 57–89.'
  ieee: J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Continuous and discrete Noether’s
    fractional conserved quantities for restricted calculus of variations,” <i>AIMS</i>,
    vol. 14(1), pp. 57–89, 2022.
  mla: Cresson, Jacky, et al. “Continuous and Discrete Noether’s Fractional Conserved
    Quantities for Restricted Calculus of Variations.” <i>AIMS</i>, vol. 14(1), 2022,
    pp. 57–89.
  short: J. Cresson, F. Jiménez, S. Ober-Blöbaum, AIMS 14(1) (2022) 57–89.
date_created: 2022-03-24T12:26:10Z
date_updated: 2022-03-24T12:26:32Z
department:
- _id: '636'
language:
- iso: eng
page: 57-89
publication: AIMS
status: public
title: Continuous and discrete Noether's fractional conserved quantities for restricted
  calculus of variations
type: journal_article
user_id: '15694'
volume: 14(1)
year: '2022'
...
---
_id: '30861'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>We consider the problem of maximization
    of metabolite production in bacterial cells formulated as a dynamical optimal
    control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions
    are concatenations of singular and bang arcs and exhibit the chattering or <jats:italic>Fuller</jats:italic>
    phenomenon, which is problematic for applications. To avoid chattering, we introduce
    a reduced model which is still biologically relevant and retains the important
    structural features of the original problem. Using a combination of analytical
    and numerical methods, we show that the singular arc is dominant in the studied
    DOCPs and exhibits the <jats:italic>turnpike</jats:italic> property. This property
    is further used in order to design simple and realistic suboptimal control strategies.</jats:p>
author:
- first_name: Jean-Baptiste
  full_name: Caillau, Jean-Baptiste
  last_name: Caillau
- first_name: Walid
  full_name: Djema, Walid
  last_name: Djema
- first_name: Jean-Luc
  full_name: Gouzé, Jean-Luc
  last_name: Gouzé
- first_name: Sofya
  full_name: Maslovskaya, Sofya
  id: '87909'
  last_name: Maslovskaya
- first_name: Jean-Baptiste
  full_name: Pomet, Jean-Baptiste
  last_name: Pomet
citation:
  ama: Caillau J-B, Djema W, Gouzé J-L, Maslovskaya S, Pomet J-B. Turnpike Property
    in Optimal Microbial Metabolite Production. <i>Journal of Optimization Theory
    and Applications</i>. Published online 2022. doi:<a href="https://doi.org/10.1007/s10957-022-02023-0">10.1007/s10957-022-02023-0</a>
  apa: Caillau, J.-B., Djema, W., Gouzé, J.-L., Maslovskaya, S., &#38; Pomet, J.-B.
    (2022). Turnpike Property in Optimal Microbial Metabolite Production. <i>Journal
    of Optimization Theory and Applications</i>. <a href="https://doi.org/10.1007/s10957-022-02023-0">https://doi.org/10.1007/s10957-022-02023-0</a>
  bibtex: '@article{Caillau_Djema_Gouzé_Maslovskaya_Pomet_2022, title={Turnpike Property
    in Optimal Microbial Metabolite Production}, DOI={<a href="https://doi.org/10.1007/s10957-022-02023-0">10.1007/s10957-022-02023-0</a>},
    journal={Journal of Optimization Theory and Applications}, publisher={Springer
    Science and Business Media LLC}, author={Caillau, Jean-Baptiste and Djema, Walid
    and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}, year={2022}
    }'
  chicago: Caillau, Jean-Baptiste, Walid Djema, Jean-Luc Gouzé, Sofya Maslovskaya,
    and Jean-Baptiste Pomet. “Turnpike Property in Optimal Microbial Metabolite Production.”
    <i>Journal of Optimization Theory and Applications</i>, 2022. <a href="https://doi.org/10.1007/s10957-022-02023-0">https://doi.org/10.1007/s10957-022-02023-0</a>.
  ieee: 'J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, and J.-B. Pomet, “Turnpike
    Property in Optimal Microbial Metabolite Production,” <i>Journal of Optimization
    Theory and Applications</i>, 2022, doi: <a href="https://doi.org/10.1007/s10957-022-02023-0">10.1007/s10957-022-02023-0</a>.'
  mla: Caillau, Jean-Baptiste, et al. “Turnpike Property in Optimal Microbial Metabolite
    Production.” <i>Journal of Optimization Theory and Applications</i>, Springer
    Science and Business Media LLC, 2022, doi:<a href="https://doi.org/10.1007/s10957-022-02023-0">10.1007/s10957-022-02023-0</a>.
  short: J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, J.-B. Pomet, Journal
    of Optimization Theory and Applications (2022).
date_created: 2022-04-08T17:23:13Z
date_updated: 2022-04-08T18:23:02Z
department:
- _id: '636'
doi: 10.1007/s10957-022-02023-0
keyword:
- Applied Mathematics
- Management Science and Operations Research
- Control and Optimization
language:
- iso: eng
publication: Journal of Optimization Theory and Applications
publication_identifier:
  issn:
  - 0022-3239
  - 1573-2878
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Turnpike Property in Optimal Microbial Metabolite Production
type: journal_article
user_id: '87909'
year: '2022'
...
---
_id: '31982'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>We show that for a generic conformal
    metric perturbation of a compact hyperbolic 3-manifold <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Sigma
    $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mi>Σ</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    with Betti number <jats:inline-formula><jats:alternatives><jats:tex-math>$$b_1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msub>\r\n
    \                   <mml:mi>b</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n
    \                 </mml:msub>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    the order of vanishing of the Ruelle zeta function at zero equals <jats:inline-formula><jats:alternatives><jats:tex-math>$$4-b_1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mn>4</mml:mn>\r\n                    <mml:mo>-</mml:mo>\r\n
    \                   <mml:msub>\r\n                      <mml:mi>b</mml:mi>\r\n
    \                     <mml:mn>1</mml:mn>\r\n                    </mml:msub>\r\n
    \                 </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    while in the hyperbolic case it is equal to <jats:inline-formula><jats:alternatives><jats:tex-math>$$4-2b_1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mn>4</mml:mn>\r\n                    <mml:mo>-</mml:mo>\r\n
    \                   <mml:mn>2</mml:mn>\r\n                    <mml:msub>\r\n                      <mml:mi>b</mml:mi>\r\n
    \                     <mml:mn>1</mml:mn>\r\n                    </mml:msub>\r\n
    \                 </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>.
    This is in contrast to the 2-dimensional case where the order of vanishing is
    a topological invariant. The proof uses the microlocal approach to dynamical zeta
    functions, giving a geometric description of generalized Pollicott–Ruelle resonant
    differential forms at 0 in the hyperbolic case and using first variation for the
    perturbation. To show that the first variation is generically nonzero we introduce
    a new identity relating pushforwards of products of resonant and coresonant 2-forms
    on the sphere bundle <jats:inline-formula><jats:alternatives><jats:tex-math>$$S\\Sigma
    $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mi>Σ</mml:mi>\r\n
    \                 </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    with harmonic 1-forms on <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Sigma
    $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mi>Σ</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula>.</jats:p>"
author:
- first_name: Mihajlo
  full_name: Cekić, Mihajlo
  last_name: Cekić
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Semyon
  full_name: Dyatlov, Semyon
  last_name: Dyatlov
- first_name: Gabriel P.
  full_name: Paternain, Gabriel P.
  last_name: Paternain
citation:
  ama: Cekić M, Delarue B, Dyatlov S, Paternain GP. The Ruelle zeta function at zero
    for nearly hyperbolic 3-manifolds. <i>Inventiones mathematicae</i>. 2022;229(1):303-394.
    doi:<a href="https://doi.org/10.1007/s00222-022-01108-x">10.1007/s00222-022-01108-x</a>
  apa: Cekić, M., Delarue, B., Dyatlov, S., &#38; Paternain, G. P. (2022). The Ruelle
    zeta function at zero for nearly hyperbolic 3-manifolds. <i>Inventiones Mathematicae</i>,
    <i>229</i>(1), 303–394. <a href="https://doi.org/10.1007/s00222-022-01108-x">https://doi.org/10.1007/s00222-022-01108-x</a>
  bibtex: '@article{Cekić_Delarue_Dyatlov_Paternain_2022, title={The Ruelle zeta function
    at zero for nearly hyperbolic 3-manifolds}, volume={229}, DOI={<a href="https://doi.org/10.1007/s00222-022-01108-x">10.1007/s00222-022-01108-x</a>},
    number={1}, journal={Inventiones mathematicae}, publisher={Springer Science and
    Business Media LLC}, author={Cekić, Mihajlo and Delarue, Benjamin and Dyatlov,
    Semyon and Paternain, Gabriel P.}, year={2022}, pages={303–394} }'
  chicago: 'Cekić, Mihajlo, Benjamin Delarue, Semyon Dyatlov, and Gabriel P. Paternain.
    “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” <i>Inventiones
    Mathematicae</i> 229, no. 1 (2022): 303–94. <a href="https://doi.org/10.1007/s00222-022-01108-x">https://doi.org/10.1007/s00222-022-01108-x</a>.'
  ieee: 'M. Cekić, B. Delarue, S. Dyatlov, and G. P. Paternain, “The Ruelle zeta function
    at zero for nearly hyperbolic 3-manifolds,” <i>Inventiones mathematicae</i>, vol.
    229, no. 1, pp. 303–394, 2022, doi: <a href="https://doi.org/10.1007/s00222-022-01108-x">10.1007/s00222-022-01108-x</a>.'
  mla: Cekić, Mihajlo, et al. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic
    3-Manifolds.” <i>Inventiones Mathematicae</i>, vol. 229, no. 1, Springer Science
    and Business Media LLC, 2022, pp. 303–94, doi:<a href="https://doi.org/10.1007/s00222-022-01108-x">10.1007/s00222-022-01108-x</a>.
  short: M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae
    229 (2022) 303–394.
date_created: 2022-06-20T08:24:17Z
date_updated: 2022-06-21T11:55:15Z
department:
- _id: '548'
doi: 10.1007/s00222-022-01108-x
intvolume: '       229'
issue: '1'
keyword:
- General Mathematics
language:
- iso: eng
page: 303-394
publication: Inventiones mathematicae
publication_identifier:
  issn:
  - 0020-9910
  - 1432-1297
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
type: journal_article
user_id: '70575'
volume: 229
year: '2022'
...
---
_id: '32233'
author:
- first_name: Uta
  full_name: Häsel-Weide, Uta
  id: '60267'
  last_name: Häsel-Weide
- first_name: Melina
  full_name: Wallner, Melina
  id: '45445'
  last_name: Wallner
- first_name: M.
  full_name: Hattermann, M.
  last_name: Hattermann
citation:
  ama: 'Häsel-Weide U, Wallner M, Hattermann M. Symmetrieverständnis von Anfang an.
    In: Gutzmann M, Carle U, Grundschulverband e. V., eds. <i>Anfangsunterricht für
    alle Kinder - Willkommen in der Schule!</i>. ; 2022:200-215.'
  apa: Häsel-Weide, U., Wallner, M., &#38; Hattermann, M. (2022). Symmetrieverständnis
    von Anfang an. In M. Gutzmann, U. Carle, &#38; Grundschulverband e. V. (Eds.),
    <i>Anfangsunterricht für alle Kinder - Willkommen in der Schule!</i> (pp. 200–215).
  bibtex: '@inbook{Häsel-Weide_Wallner_Hattermann_2022, place={Frankfurt a. M.}, title={Symmetrieverständnis
    von Anfang an}, booktitle={Anfangsunterricht für alle Kinder - Willkommen in der
    Schule!}, author={Häsel-Weide, Uta and Wallner, Melina and Hattermann, M.}, editor={Gutzmann,
    M. and Carle, U. and Grundschulverband e. V.}, year={2022}, pages={200–215} }'
  chicago: Häsel-Weide, Uta, Melina Wallner, and M. Hattermann. “Symmetrieverständnis
    von Anfang an.” In <i>Anfangsunterricht für alle Kinder - Willkommen in der Schule!</i>,
    edited by M. Gutzmann, U. Carle, and Grundschulverband e. V., 200–215. Frankfurt
    a. M., 2022.
  ieee: U. Häsel-Weide, M. Wallner, and M. Hattermann, “Symmetrieverständnis von Anfang
    an,” in <i>Anfangsunterricht für alle Kinder - Willkommen in der Schule!</i>,
    M. Gutzmann, U. Carle, and Grundschulverband e. V., Eds. Frankfurt a. M., 2022,
    pp. 200–215.
  mla: Häsel-Weide, Uta, et al. “Symmetrieverständnis von Anfang an.” <i>Anfangsunterricht
    für alle Kinder - Willkommen in der Schule!</i>, edited by M. Gutzmann et al.,
    2022, pp. 200–15.
  short: 'U. Häsel-Weide, M. Wallner, M. Hattermann, in: M. Gutzmann, U. Carle, Grundschulverband
    e. V. (Eds.), Anfangsunterricht für alle Kinder - Willkommen in der Schule!, Frankfurt
    a. M., 2022, pp. 200–215.'
corporate_editor:
- Grundschulverband e. V.
date_created: 2022-06-28T06:30:12Z
date_updated: 2022-07-05T06:48:40Z
department:
- _id: '98'
- _id: '543'
editor:
- first_name: M.
  full_name: Gutzmann, M.
  last_name: Gutzmann
- first_name: U.
  full_name: Carle, U.
  last_name: Carle
language:
- iso: ger
page: 200-215
place: Frankfurt a. M.
publication: Anfangsunterricht für alle Kinder - Willkommen in der Schule!
publication_status: published
status: public
title: Symmetrieverständnis von Anfang an
type: book_chapter
user_id: '45445'
year: '2022'
...
---
_id: '32339'
author:
- first_name: Uta
  full_name: Häsel-Weide, Uta
  id: '60267'
  last_name: Häsel-Weide
- first_name: S.
  full_name: Seitz, S.
  last_name: Seitz
- first_name: Melina
  full_name: Wallner, Melina
  id: '45445'
  last_name: Wallner
- first_name: Y.
  full_name: Wilke, Y.
  last_name: Wilke
citation:
  ama: 'Häsel-Weide U, Seitz S, Wallner M, Wilke Y. Professionalisierung für inklusiven
    Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung
    angehender Mathematiklehrkräfte in der Sekundarstufe. In: Lutz D, Becker J, Buchhaupt
    F, Katzenbach D, Strecker A, Urban M, eds. <i>Qualifizierung für Inklusion. Sekundarstufe</i>.
    Waxmann; 2022:83-100.'
  apa: Häsel-Weide, U., Seitz, S., Wallner, M., &#38; Wilke, Y. (2022). Professionalisierung
    für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven
    Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe. In
    D. Lutz, J. Becker, F. Buchhaupt, D. Katzenbach, A. Strecker, &#38; M. Urban (Eds.),
    <i>Qualifizierung für Inklusion. Sekundarstufe</i> (pp. 83–100). Waxmann.
  bibtex: '@inbook{Häsel-Weide_Seitz_Wallner_Wilke_2022, place={Münster}, title={Professionalisierung
    für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven
    Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe}, booktitle={Qualifizierung
    für Inklusion. Sekundarstufe}, publisher={Waxmann}, author={Häsel-Weide, Uta and
    Seitz, S. and Wallner, Melina and Wilke, Y.}, editor={Lutz, D. and Becker, J.
    and Buchhaupt, F. and Katzenbach, D. and Strecker, A. and Urban, M.}, year={2022},
    pages={83–100} }'
  chicago: 'Häsel-Weide, Uta, S. Seitz, Melina Wallner, and Y. Wilke. “Professionalisierung
    für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven
    Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe.” In
    <i>Qualifizierung für Inklusion. Sekundarstufe</i>, edited by D. Lutz, J. Becker,
    F. Buchhaupt, D. Katzenbach, A. Strecker, and M. Urban, 83–100. Münster: Waxmann,
    2022.'
  ieee: 'U. Häsel-Weide, S. Seitz, M. Wallner, and Y. Wilke, “Professionalisierung
    für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven
    Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe,” in
    <i>Qualifizierung für Inklusion. Sekundarstufe</i>, D. Lutz, J. Becker, F. Buchhaupt,
    D. Katzenbach, A. Strecker, and M. Urban, Eds. Münster: Waxmann, 2022, pp. 83–100.'
  mla: Häsel-Weide, Uta, et al. “Professionalisierung für inklusiven Mathematikunterricht.
    Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender
    Mathematiklehrkräfte in der Sekundarstufe.” <i>Qualifizierung für Inklusion. Sekundarstufe</i>,
    edited by D. Lutz et al., Waxmann, 2022, pp. 83–100.
  short: 'U. Häsel-Weide, S. Seitz, M. Wallner, Y. Wilke, in: D. Lutz, J. Becker,
    F. Buchhaupt, D. Katzenbach, A. Strecker, M. Urban (Eds.), Qualifizierung für
    Inklusion. Sekundarstufe, Waxmann, Münster, 2022, pp. 83–100.'
date_created: 2022-07-11T05:31:28Z
date_updated: 2022-07-11T05:31:46Z
department:
- _id: '98'
- _id: '543'
editor:
- first_name: D.
  full_name: Lutz, D.
  last_name: Lutz
- first_name: J.
  full_name: Becker, J.
  last_name: Becker
- first_name: F.
  full_name: Buchhaupt, F.
  last_name: Buchhaupt
- first_name: D.
  full_name: Katzenbach, D.
  last_name: Katzenbach
- first_name: A.
  full_name: Strecker, A.
  last_name: Strecker
- first_name: M.
  full_name: Urban, M.
  last_name: Urban
language:
- iso: ger
page: 83-100
place: Münster
publication: Qualifizierung für Inklusion. Sekundarstufe
publication_status: published
publisher: Waxmann
status: public
title: Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre
  Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte
  in der Sekundarstufe
type: book_chapter
user_id: '85821'
year: '2022'
...
---
_id: '32338'
author:
- first_name: K.
  full_name: Hähn, K.
  last_name: Hähn
- first_name: Uta
  full_name: Häsel-Weide, Uta
  id: '60267'
  last_name: Häsel-Weide
- first_name: P.
  full_name: Scherer, P.
  last_name: Scherer
citation:
  ama: Hähn K, Häsel-Weide U, Scherer P. Diagnosegeleitete Förderung im inklusiven
    Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte
    Handlungspraxis in der Lehrer*innenbildung. <i>QfI - Qualifizierung für Inklusion</i>.
    2022;3(2).
  apa: Hähn, K., Häsel-Weide, U., &#38; Scherer, P. (2022). Diagnosegeleitete Förderung
    im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch
    reflektierte Handlungspraxis in der Lehrer*innenbildung. <i>QfI - Qualifizierung
    für Inklusion</i>, <i>3</i>(2).
  bibtex: '@article{Hähn_Häsel-Weide_Scherer_2022, title={Diagnosegeleitete Förderung
    im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch
    reflektierte Handlungspraxis in der Lehrer*innenbildung.}, volume={3}, number={2},
    journal={QfI - Qualifizierung für Inklusion}, author={Hähn, K. and Häsel-Weide,
    Uta and Scherer, P.}, year={2022} }'
  chicago: Hähn, K., Uta Häsel-Weide, and P. Scherer. “Diagnosegeleitete Förderung
    im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch
    reflektierte Handlungspraxis in der Lehrer*innenbildung.” <i>QfI - Qualifizierung
    für Inklusion</i> 3, no. 2 (2022).
  ieee: K. Hähn, U. Häsel-Weide, and P. Scherer, “Diagnosegeleitete Förderung im inklusiven
    Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte
    Handlungspraxis in der Lehrer*innenbildung.,” <i>QfI - Qualifizierung für Inklusion</i>,
    vol. 3, no. 2, 2022.
  mla: Hähn, K., et al. “Diagnosegeleitete Förderung im inklusiven Mathematikunterricht
    der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der
    Lehrer*innenbildung.” <i>QfI - Qualifizierung für Inklusion</i>, vol. 3, no. 2,
    2022.
  short: K. Hähn, U. Häsel-Weide, P. Scherer, QfI - Qualifizierung für Inklusion 3
    (2022).
date_created: 2022-07-11T05:13:52Z
date_updated: 2022-07-11T05:31:41Z
department:
- _id: '98'
- _id: '543'
intvolume: '         3'
issue: '2'
language:
- iso: ger
publication: QfI - Qualifizierung für Inklusion
publication_status: published
related_material:
  link:
  - relation: contains
    url: https://doi.org/10.21248/qfi.72
status: public
title: Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule
  – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.
type: journal_article
user_id: '85821'
volume: 3
year: '2022'
...
---
_id: '29673'
abstract:
- lang: eng
  text: Koopman operator theory has been successfully applied to problems from various
    research areas such as fluid dynamics, molecular dynamics, climate science, engineering,
    and biology. Applications include detecting metastable or coherent sets, coarse-graining,
    system identification, and control. There is an intricate connection between dynamical
    systems driven by stochastic differential equations and quantum mechanics. In
    this paper, we compare the ground-state transformation and Nelson's stochastic
    mechanics and demonstrate how data-driven methods developed for the approximation
    of the Koopman operator can be used to analyze quantum physics problems. Moreover,
    we exploit the relationship between Schrödinger operators and stochastic control
    problems to show that modern data-driven methods for stochastic control can be
    used to solve the stationary or imaginary-time Schrödinger equation. Our findings
    open up a new avenue towards solving Schrödinger's equation using recently developed
    tools from data science.
author:
- first_name: Stefan
  full_name: Klus, Stefan
  last_name: Klus
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
citation:
  ama: 'Klus S, Nüske F, Peitz S. Koopman analysis of quantum systems. <i>Journal
    of Physics A: Mathematical and Theoretical</i>. 2022;55(31):314002. doi:<a href="https://doi.org/10.1088/1751-8121/ac7d22">10.1088/1751-8121/ac7d22</a>'
  apa: 'Klus, S., Nüske, F., &#38; Peitz, S. (2022). Koopman analysis of quantum systems.
    <i>Journal of Physics A: Mathematical and Theoretical</i>, <i>55</i>(31), 314002.
    <a href="https://doi.org/10.1088/1751-8121/ac7d22">https://doi.org/10.1088/1751-8121/ac7d22</a>'
  bibtex: '@article{Klus_Nüske_Peitz_2022, title={Koopman analysis of quantum systems},
    volume={55}, DOI={<a href="https://doi.org/10.1088/1751-8121/ac7d22">10.1088/1751-8121/ac7d22</a>},
    number={31}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP
    Publishing Ltd.}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian},
    year={2022}, pages={314002} }'
  chicago: 'Klus, Stefan, Feliks Nüske, and Sebastian Peitz. “Koopman Analysis of
    Quantum Systems.” <i>Journal of Physics A: Mathematical and Theoretical</i> 55,
    no. 31 (2022): 314002. <a href="https://doi.org/10.1088/1751-8121/ac7d22">https://doi.org/10.1088/1751-8121/ac7d22</a>.'
  ieee: 'S. Klus, F. Nüske, and S. Peitz, “Koopman analysis of quantum systems,” <i>Journal
    of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 31, p. 314002, 2022,
    doi: <a href="https://doi.org/10.1088/1751-8121/ac7d22">10.1088/1751-8121/ac7d22</a>.'
  mla: 'Klus, Stefan, et al. “Koopman Analysis of Quantum Systems.” <i>Journal of
    Physics A: Mathematical and Theoretical</i>, vol. 55, no. 31, IOP Publishing Ltd.,
    2022, p. 314002, doi:<a href="https://doi.org/10.1088/1751-8121/ac7d22">10.1088/1751-8121/ac7d22</a>.'
  short: 'S. Klus, F. Nüske, S. Peitz, Journal of Physics A: Mathematical and Theoretical
    55 (2022) 314002.'
date_created: 2022-01-31T09:49:40Z
date_updated: 2022-07-18T14:26:41Z
department:
- _id: '655'
- _id: '101'
doi: 10.1088/1751-8121/ac7d22
external_id:
  arxiv:
  - '2201.12062'
intvolume: '        55'
issue: '31'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://iopscience.iop.org/article/10.1088/1751-8121/ac7d22/pdf
oa: '1'
page: '314002'
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_status: published
publisher: IOP Publishing Ltd.
status: public
title: Koopman analysis of quantum systems
type: journal_article
user_id: '47427'
volume: 55
year: '2022'
...
---
_id: '34618'
abstract:
- lang: eng
  text: "In this article, we show how second-order derivative information can be\r\nincorporated
    into gradient sampling methods for nonsmooth optimization. The\r\nsecond-order
    information we consider is essentially the set of coefficients of\r\nall second-order
    Taylor expansions of the objective in a closed ball around a\r\ngiven point. Based
    on this concept, we define a model of the objective as the\r\nmaximum of these
    Taylor expansions. Iteratively minimizing this model\r\n(constrained to the closed
    ball) results in a simple descent method, for which\r\nwe prove convergence to
    minimal points in case the objective is convex. To\r\nobtain an implementable
    method, we construct an approximation scheme for the\r\nsecond-order information
    based on sampling objective values, gradients and\r\nHessian matrices at finitely
    many points. Using a set of test problems, we\r\ncompare the resulting method
    to five other available solvers. Considering the\r\nnumber of function evaluations,
    the results suggest that the method we propose\r\nis superior to the standard
    gradient sampling method, and competitive compared\r\nto other methods."
author:
- first_name: Bennet
  full_name: Gebken, Bennet
  id: '32643'
  last_name: Gebken
citation:
  ama: Gebken B. Using second-order information in gradient sampling methods for 
    nonsmooth optimization. <i>arXiv:221004579</i>. Published online 2022.
  apa: Gebken, B. (2022). Using second-order information in gradient sampling methods
    for  nonsmooth optimization. In <i>arXiv:2210.04579</i>.
  bibtex: '@article{Gebken_2022, title={Using second-order information in gradient
    sampling methods for  nonsmooth optimization}, journal={arXiv:2210.04579}, author={Gebken,
    Bennet}, year={2022} }'
  chicago: Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods
    for  Nonsmooth Optimization.” <i>ArXiv:2210.04579</i>, 2022.
  ieee: B. Gebken, “Using second-order information in gradient sampling methods for 
    nonsmooth optimization,” <i>arXiv:2210.04579</i>. 2022.
  mla: Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods
    for  Nonsmooth Optimization.” <i>ArXiv:2210.04579</i>, 2022.
  short: B. Gebken, ArXiv:2210.04579 (2022).
date_created: 2022-12-20T15:25:17Z
date_updated: 2022-12-20T15:28:54Z
department:
- _id: '101'
external_id:
  arxiv:
  - '2210.04579'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/pdf/2210.04579
oa: '1'
publication: arXiv:2210.04579
status: public
title: Using second-order information in gradient sampling methods for  nonsmooth
  optimization
type: preprint
user_id: '32643'
year: '2022'
...
---
_id: '34792'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Non-Lie subgroups in Lie groups over local fields of positive characteristic.
    <i>p-Adic Numbers, Ultrametric Analysis, and Applications</i>. 2022;14(2):138–144.
    doi:<a href="https://doi.org/10.1134/S2070046622020042">10.1134/S2070046622020042</a>
  apa: Glöckner, H. (2022). Non-Lie subgroups in Lie groups over local fields of positive
    characteristic. <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>,
    <i>14</i>(2), 138–144. <a href="https://doi.org/10.1134/S2070046622020042">https://doi.org/10.1134/S2070046622020042</a>
  bibtex: '@article{Glöckner_2022, title={Non-Lie subgroups in Lie groups over local
    fields of positive characteristic}, volume={14}, DOI={<a href="https://doi.org/10.1134/S2070046622020042">10.1134/S2070046622020042</a>},
    number={2}, journal={p-Adic Numbers, Ultrametric Analysis, and Applications},
    author={Glöckner, Helge}, year={2022}, pages={138–144} }'
  chicago: 'Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of
    Positive Characteristic.” <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>
    14, no. 2 (2022): 138–144. <a href="https://doi.org/10.1134/S2070046622020042">https://doi.org/10.1134/S2070046622020042</a>.'
  ieee: 'H. Glöckner, “Non-Lie subgroups in Lie groups over local fields of positive
    characteristic,” <i>p-Adic Numbers, Ultrametric Analysis, and Applications</i>,
    vol. 14, no. 2, pp. 138–144, 2022, doi: <a href="https://doi.org/10.1134/S2070046622020042">10.1134/S2070046622020042</a>.'
  mla: Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of Positive
    Characteristic.” <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>,
    vol. 14, no. 2, 2022, pp. 138–144, doi:<a href="https://doi.org/10.1134/S2070046622020042">10.1134/S2070046622020042</a>.
  short: H. Glöckner, P-Adic Numbers, Ultrametric Analysis, and Applications 14 (2022)
    138–144.
date_created: 2022-12-21T19:27:51Z
date_updated: 2022-12-21T19:30:25Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1134/S2070046622020042
intvolume: '        14'
issue: '2'
keyword:
- 20Exx
- 22Exx
- 32Cxx
language:
- iso: eng
page: 138–144
publication: p-Adic Numbers, Ultrametric Analysis, and Applications
publication_identifier:
  issn:
  - 2070-0466
quality_controlled: '1'
status: public
title: Non-Lie subgroups in Lie groups over local fields of positive characteristic
type: journal_article
user_id: '178'
volume: 14
year: '2022'
...
---
_id: '34791'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: Alexander
  full_name: Schmeding, Alexander
  last_name: Schmeding
citation:
  ama: Glöckner H, Schmeding A. Manifolds of mappings on Cartesian products. <i>Annals
    of Global Analysis and Geometry</i>. 2022;61(2):359–398. doi:<a href="https://doi.org/10.1007/s10455-021-09816-y">10.1007/s10455-021-09816-y</a>
  apa: Glöckner, H., &#38; Schmeding, A. (2022). Manifolds of mappings on Cartesian
    products. <i>Annals of Global Analysis and Geometry</i>, <i>61</i>(2), 359–398.
    <a href="https://doi.org/10.1007/s10455-021-09816-y">https://doi.org/10.1007/s10455-021-09816-y</a>
  bibtex: '@article{Glöckner_Schmeding_2022, title={Manifolds of mappings on Cartesian
    products}, volume={61}, DOI={<a href="https://doi.org/10.1007/s10455-021-09816-y">10.1007/s10455-021-09816-y</a>},
    number={2}, journal={Annals of Global Analysis and Geometry}, author={Glöckner,
    Helge and Schmeding, Alexander}, year={2022}, pages={359–398} }'
  chicago: 'Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian
    Products.” <i>Annals of Global Analysis and Geometry</i> 61, no. 2 (2022): 359–398.
    <a href="https://doi.org/10.1007/s10455-021-09816-y">https://doi.org/10.1007/s10455-021-09816-y</a>.'
  ieee: 'H. Glöckner and A. Schmeding, “Manifolds of mappings on Cartesian products,”
    <i>Annals of Global Analysis and Geometry</i>, vol. 61, no. 2, pp. 359–398, 2022,
    doi: <a href="https://doi.org/10.1007/s10455-021-09816-y">10.1007/s10455-021-09816-y</a>.'
  mla: Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian
    Products.” <i>Annals of Global Analysis and Geometry</i>, vol. 61, no. 2, 2022,
    pp. 359–398, doi:<a href="https://doi.org/10.1007/s10455-021-09816-y">10.1007/s10455-021-09816-y</a>.
  short: H. Glöckner, A. Schmeding, Annals of Global Analysis and Geometry 61 (2022)
    359–398.
date_created: 2022-12-21T19:24:48Z
date_updated: 2022-12-21T19:27:09Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1007/s10455-021-09816-y
intvolume: '        61'
issue: '2'
keyword:
- 58D15
- '22E65'
- '26E15'
- '26E20'
- '46E40'
- 46T20
- 58A05
language:
- iso: eng
page: 359–398
publication: Annals of Global Analysis and Geometry
publication_identifier:
  issn:
  - 0232-704X
quality_controlled: '1'
status: public
title: Manifolds of mappings on Cartesian products
type: journal_article
user_id: '178'
volume: 61
year: '2022'
...
---
_id: '34796'
abstract:
- lang: eng
  text: 'We prove various results in infinite-dimensional differential calculus that
    relate the differentiability properties of functions and associated operator-valued
    functions (e.g., differentials). The results are applied in two areas: (1) in
    the theory of infinite-dimensional vector bundles, to construct new bundles from
    given ones, such as dual bundles, topological tensor products, infinite direct
    sums, and completions (under suitable hypotheses); (2) in the theory of locally
    convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity
    of passage from a function to the associated Hamiltonian vector field. Topological
    properties of topological vector spaces are essential for the studies, which allow
    the hypocontinuity of bilinear mappings to be exploited. Notably, we encounter
    kR-spaces and locally convex spaces E such that E&times;E is a kR-space.'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Aspects of differential calculus related to infinite-dimensional
    vector bundles and Poisson vector spaces. <i>Axioms</i>. 2022;11(5). doi:<a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>
  apa: Glöckner, H. (2022). Aspects of differential calculus related to infinite-dimensional
    vector bundles and Poisson vector spaces. <i>Axioms</i>, <i>11</i>(5). <a href="https://doi.org/10.3390/axioms11050221">https://doi.org/10.3390/axioms11050221</a>
  bibtex: '@article{Glöckner_2022, title={Aspects of differential calculus related
    to infinite-dimensional vector bundles and Poisson vector spaces}, volume={11},
    DOI={<a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>},
    number={5}, journal={Axioms}, author={Glöckner, Helge}, year={2022} }'
  chicago: Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional
    Vector Bundles and Poisson Vector Spaces.” <i>Axioms</i> 11, no. 5 (2022). <a
    href="https://doi.org/10.3390/axioms11050221">https://doi.org/10.3390/axioms11050221</a>.
  ieee: 'H. Glöckner, “Aspects of differential calculus related to infinite-dimensional
    vector bundles and Poisson vector spaces,” <i>Axioms</i>, vol. 11, no. 5, 2022,
    doi: <a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>.'
  mla: Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional
    Vector Bundles and Poisson Vector Spaces.” <i>Axioms</i>, vol. 11, no. 5, 2022,
    doi:<a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>.
  short: H. Glöckner, Axioms 11 (2022).
date_created: 2022-12-21T20:02:29Z
date_updated: 2022-12-22T07:31:55Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.3390/axioms11050221
intvolume: '        11'
issue: '5'
language:
- iso: eng
publication: Axioms
publication_identifier:
  issn:
  - 2075-1680
quality_controlled: '1'
status: public
title: Aspects of differential calculus related to infinite-dimensional vector bundles
  and Poisson vector spaces
type: journal_article
user_id: '178'
volume: 11
year: '2022'
...
---
_id: '34804'
abstract:
- lang: eng
  text: "Starting with a finite-dimensional complex Lie algebra, we extend scalars\r\nusing
    suitable commutative topological algebras. We study Birkhoff\r\ndecompositions
    for the corresponding loop groups. Some results remain valid for\r\nloop groups
    with valued in complex Banach-Lie groups."
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Birkhoff decompositions for loop groups with coefficient algebras.
    <i>arXiv:220611711</i>. Published online 2022.
  apa: Glöckner, H. (2022). Birkhoff decompositions for loop groups with coefficient
    algebras. In <i>arXiv:2206.11711</i>.
  bibtex: '@article{Glöckner_2022, title={Birkhoff decompositions for loop groups
    with coefficient algebras}, journal={arXiv:2206.11711}, author={Glöckner, Helge},
    year={2022} }'
  chicago: Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient
    Algebras.” <i>ArXiv:2206.11711</i>, 2022.
  ieee: H. Glöckner, “Birkhoff decompositions for loop groups with coefficient algebras,”
    <i>arXiv:2206.11711</i>. 2022.
  mla: Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient
    Algebras.” <i>ArXiv:2206.11711</i>, 2022.
  short: H. Glöckner, ArXiv:2206.11711 (2022).
date_created: 2022-12-22T07:42:07Z
date_updated: 2022-12-22T07:44:08Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
  arxiv:
  - '2206.11711'
language:
- iso: eng
publication: arXiv:2206.11711
status: public
title: Birkhoff decompositions for loop groups with coefficient algebras
type: preprint
user_id: '178'
year: '2022'
...
---
_id: '31556'
abstract:
- lang: ger
  text: Mehrzieloptimierung behandelt Probleme, bei denen mehrere skalare Zielfunktionen
    simultan optimiert werden sollen. Ein Punkt ist in diesem Fall optimal, wenn es
    keinen anderen Punkt gibt, der mindestens genauso gut ist in allen Zielfunktionen
    und besser in mindestens einer Zielfunktion. Ein notwendiges Optimalitätskriterium
    lässt sich über Ableitungsinformationen erster Ordnung der Zielfunktionen herleiten.
    Die Menge der Punkte, die dieses notwendige Kriterium erfüllen, wird als Pareto-kritische
    Menge bezeichnet. Diese Arbeit enthält neue Resultate über Pareto-kritische Mengen
    für glatte und nicht-glatte Mehrzieloptimierungsprobleme, sowohl was deren Berechnung
    betrifft als auch deren Struktur. Im glatten Fall erfolgt die Berechnung über
    ein Fortsetzungsverfahren, im nichtglatten Fall über ein Abstiegsverfahren. Anschließend
    wird die Struktur des Randes der Pareto-kritischen Menge analysiert, welcher aus
    Pareto-kritischen Mengen kleinerer Subprobleme besteht. Schlussendlich werden
    inverse Probleme betrachtet, bei denen zu einer gegebenen Datenmenge ein Zielfunktionsvektor
    gefunden werden soll, für den die Datenpunkte kritisch sind.
- lang: eng
  text: Multiobjective optimization is concerned with the simultaneous optimization
    of multiple scalar-valued functions. In this case, a point is optimal if there
    is no other point that is at least as good in all objectives and better in at
    least one objective. A necessary condition for optimality can be derived based
    on first-order information of the objectives. The set of points that satisfy this
    necessary condition is called the Pareto critical set. This thesis presents new
    results about Pareto critical sets for smooth and nonsmooth multiobjective optimization
    problems, both in terms of their efficient computation and structural properties.
    In the smooth case they are computed via a continuation method and in the nonsmooth
    case via a descent method. Afterwards, the structure of the boundary of the Pareto
    critical set is analyzed, which consists of Pareto critical sets of smaller subproblems.
    Finally, inverse problems are considered, where a data set is given and an objective
    vector is sought for which the data points are critical.
author:
- first_name: Bennet
  full_name: Gebken, Bennet
  id: '32643'
  last_name: Gebken
citation:
  ama: Gebken B. <i>Computation and Analysis of Pareto Critical Sets in Smooth and
    Nonsmooth Multiobjective Optimization</i>.; 2022. doi:<a href="https://doi.org/10.17619/UNIPB/1-1327">10.17619/UNIPB/1-1327</a>
  apa: Gebken, B. (2022). <i>Computation and analysis of Pareto critical sets in smooth
    and nonsmooth multiobjective optimization</i>. <a href="https://doi.org/10.17619/UNIPB/1-1327">https://doi.org/10.17619/UNIPB/1-1327</a>
  bibtex: '@book{Gebken_2022, title={Computation and analysis of Pareto critical sets
    in smooth and nonsmooth multiobjective optimization}, DOI={<a href="https://doi.org/10.17619/UNIPB/1-1327">10.17619/UNIPB/1-1327</a>},
    author={Gebken, Bennet}, year={2022} }'
  chicago: Gebken, Bennet. <i>Computation and Analysis of Pareto Critical Sets in
    Smooth and Nonsmooth Multiobjective Optimization</i>, 2022. <a href="https://doi.org/10.17619/UNIPB/1-1327">https://doi.org/10.17619/UNIPB/1-1327</a>.
  ieee: B. Gebken, <i>Computation and analysis of Pareto critical sets in smooth and
    nonsmooth multiobjective optimization</i>. 2022.
  mla: Gebken, Bennet. <i>Computation and Analysis of Pareto Critical Sets in Smooth
    and Nonsmooth Multiobjective Optimization</i>. 2022, doi:<a href="https://doi.org/10.17619/UNIPB/1-1327">10.17619/UNIPB/1-1327</a>.
  short: B. Gebken, Computation and Analysis of Pareto Critical Sets in Smooth and
    Nonsmooth Multiobjective Optimization, 2022.
date_created: 2022-06-01T06:48:08Z
date_updated: 2022-06-01T07:13:09Z
department:
- _id: '101'
doi: 10.17619/UNIPB/1-1327
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://digital.ub.uni-paderborn.de/hs/download/pdf/6531779
oa: '1'
status: public
supervisor:
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
title: Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective
  optimization
type: dissertation
user_id: '32643'
year: '2022'
...
---
_id: '33150'
abstract:
- lang: eng
  text: In this article, we build on previous work to present an optimization algorithm
    for nonlinearly constrained multi-objective optimization problems. The algorithm
    combines a surrogate-assisted derivative-free trust-region approach with the filter
    method known from single-objective optimization. Instead of the true objective
    and constraint functions, so-called fully linear models are employed and we show
    how to deal with the gradient inexactness in the composite step setting, adapted
    from single-objective optimization as well. Under standard assumptions, we prove
    convergence of a subset of iterates to a quasi-stationary point and if constraint
    qualifications hold, then the limit point is also a KKT-point of the multi-objective
    problem.
author:
- first_name: Manuel Bastian
  full_name: Berkemeier, Manuel Bastian
  id: '51701'
  last_name: Berkemeier
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
citation:
  ama: Berkemeier MB, Peitz S. Multi-Objective Trust-Region Filter Method for Nonlinear
    Constraints using Inexact Gradients. <i>arXiv:220812094</i>. Published online
    2022.
  apa: Berkemeier, M. B., &#38; Peitz, S. (2022). Multi-Objective Trust-Region Filter
    Method for Nonlinear Constraints using Inexact Gradients. In <i>arXiv:2208.12094</i>.
  bibtex: '@article{Berkemeier_Peitz_2022, title={Multi-Objective Trust-Region Filter
    Method for Nonlinear Constraints using Inexact Gradients}, journal={arXiv:2208.12094},
    author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2022} }'
  chicago: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region
    Filter Method for Nonlinear Constraints Using Inexact Gradients.” <i>ArXiv:2208.12094</i>,
    2022.
  ieee: M. B. Berkemeier and S. Peitz, “Multi-Objective Trust-Region Filter Method
    for Nonlinear Constraints using Inexact Gradients,” <i>arXiv:2208.12094</i>. 2022.
  mla: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region
    Filter Method for Nonlinear Constraints Using Inexact Gradients.” <i>ArXiv:2208.12094</i>,
    2022.
  short: M.B. Berkemeier, S. Peitz, ArXiv:2208.12094 (2022).
date_created: 2022-08-26T06:08:06Z
date_updated: 2022-08-26T06:12:10Z
department:
- _id: '101'
- _id: '655'
external_id:
  arxiv:
  - '2208.12094'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/pdf/2208.12094
oa: '1'
publication: arXiv:2208.12094
status: public
title: Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using
  Inexact Gradients
type: preprint
user_id: '47427'
year: '2022'
...
---
_id: '20731'
abstract:
- lang: eng
  text: We present a novel algorithm that allows us to gain detailed insight into
    the effects of sparsity in linear and nonlinear optimization, which is of great
    importance in many scientific areas such as image and signal processing, medical
    imaging, compressed sensing, and machine learning (e.g., for the training of neural
    networks). Sparsity is an important feature to ensure robustness against noisy
    data, but also to find models that are interpretable and easy to analyze due to
    the small number of relevant terms. It is common practice to enforce sparsity
    by adding the ℓ1-norm as a weighted penalty term. In order to gain a better understanding
    and to allow for an informed model selection, we directly solve the corresponding
    multiobjective optimization problem (MOP) that arises when we minimize the main
    objective and the ℓ1-norm simultaneously. As this MOP is in general non-convex
    for nonlinear objectives, the weighting method will fail to provide all optimal
    compromises. To avoid this issue, we present a continuation method which is specifically
    tailored to MOPs with two objective functions one of which is the ℓ1-norm. Our
    method can be seen as a generalization of well-known homotopy methods for linear
    regression problems to the nonlinear case. Several numerical examples - including
    neural network training - demonstrate our theoretical findings and the additional
    insight that can be gained by this multiobjective approach.
article_type: original
author:
- first_name: Katharina
  full_name: Bieker, Katharina
  id: '32829'
  last_name: Bieker
- first_name: Bennet
  full_name: Gebken, Bennet
  id: '32643'
  last_name: Gebken
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
citation:
  ama: Bieker K, Gebken B, Peitz S. On the Treatment of Optimization Problems with
    L1 Penalty Terms via Multiobjective Continuation. <i>IEEE Transactions on Pattern
    Analysis and Machine Intelligence</i>. 2022;44(11):7797-7808. doi:<a href="https://doi.org/10.1109/TPAMI.2021.3114962">10.1109/TPAMI.2021.3114962</a>
  apa: Bieker, K., Gebken, B., &#38; Peitz, S. (2022). On the Treatment of Optimization
    Problems with L1 Penalty Terms via Multiobjective Continuation. <i>IEEE Transactions
    on Pattern Analysis and Machine Intelligence</i>, <i>44</i>(11), 7797–7808. <a
    href="https://doi.org/10.1109/TPAMI.2021.3114962">https://doi.org/10.1109/TPAMI.2021.3114962</a>
  bibtex: '@article{Bieker_Gebken_Peitz_2022, title={On the Treatment of Optimization
    Problems with L1 Penalty Terms via Multiobjective Continuation}, volume={44},
    DOI={<a href="https://doi.org/10.1109/TPAMI.2021.3114962">10.1109/TPAMI.2021.3114962</a>},
    number={11}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
    publisher={IEEE}, author={Bieker, Katharina and Gebken, Bennet and Peitz, Sebastian},
    year={2022}, pages={7797–7808} }'
  chicago: 'Bieker, Katharina, Bennet Gebken, and Sebastian Peitz. “On the Treatment
    of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.”
    <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i> 44, no.
    11 (2022): 7797–7808. <a href="https://doi.org/10.1109/TPAMI.2021.3114962">https://doi.org/10.1109/TPAMI.2021.3114962</a>.'
  ieee: 'K. Bieker, B. Gebken, and S. Peitz, “On the Treatment of Optimization Problems
    with L1 Penalty Terms via Multiobjective Continuation,” <i>IEEE Transactions on
    Pattern Analysis and Machine Intelligence</i>, vol. 44, no. 11, pp. 7797–7808,
    2022, doi: <a href="https://doi.org/10.1109/TPAMI.2021.3114962">10.1109/TPAMI.2021.3114962</a>.'
  mla: Bieker, Katharina, et al. “On the Treatment of Optimization Problems with L1
    Penalty Terms via Multiobjective Continuation.” <i>IEEE Transactions on Pattern
    Analysis and Machine Intelligence</i>, vol. 44, no. 11, IEEE, 2022, pp. 7797–808,
    doi:<a href="https://doi.org/10.1109/TPAMI.2021.3114962">10.1109/TPAMI.2021.3114962</a>.
  short: K. Bieker, B. Gebken, S. Peitz, IEEE Transactions on Pattern Analysis and
    Machine Intelligence 44 (2022) 7797–7808.
date_created: 2020-12-15T07:46:36Z
date_updated: 2022-10-21T12:27:16Z
ddc:
- '510'
department:
- _id: '101'
- _id: '530'
- _id: '655'
doi: 10.1109/TPAMI.2021.3114962
file:
- access_level: closed
  content_type: application/pdf
  creator: speitz
  date_created: 2021-09-25T11:59:15Z
  date_updated: 2021-09-25T11:59:15Z
  file_id: '25040'
  file_name: On_the_Treatment_of_Optimization_Problems_with_L1_Penalty_Terms_via_Multiobjective_Continuation.pdf
  file_size: 7990831
  relation: main_file
  success: 1
file_date_updated: 2021-09-25T11:59:15Z
has_accepted_license: '1'
intvolume: '        44'
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9547772
oa: '1'
page: 7797-7808
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_status: epub_ahead
publisher: IEEE
status: public
title: On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective
  Continuation
type: journal_article
user_id: '47427'
volume: 44
year: '2022'
...
---
_id: '35306'
author:
- first_name: Yannick
  full_name: Guedes Bonthonneau, Yannick
  last_name: Guedes Bonthonneau
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: Guedes Bonthonneau Y, Weich T. Ruelle–Pollicott resonances for manifolds with
    hyperbolic cusps. <i>Journal of the European Mathematical Society</i>. 2022;24(3):851-923.
    doi:<a href="https://doi.org/10.4171/jems/1103">10.4171/jems/1103</a>
  apa: Guedes Bonthonneau, Y., &#38; Weich, T. (2022). Ruelle–Pollicott resonances
    for manifolds with hyperbolic cusps. <i>Journal of the European Mathematical Society</i>,
    <i>24</i>(3), 851–923. <a href="https://doi.org/10.4171/jems/1103">https://doi.org/10.4171/jems/1103</a>
  bibtex: '@article{Guedes Bonthonneau_Weich_2022, title={Ruelle–Pollicott resonances
    for manifolds with hyperbolic cusps}, volume={24}, DOI={<a href="https://doi.org/10.4171/jems/1103">10.4171/jems/1103</a>},
    number={3}, journal={Journal of the European Mathematical Society}, publisher={European
    Mathematical Society - EMS - Publishing House GmbH}, author={Guedes Bonthonneau,
    Yannick and Weich, Tobias}, year={2022}, pages={851–923} }'
  chicago: 'Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances
    for Manifolds with Hyperbolic Cusps.” <i>Journal of the European Mathematical
    Society</i> 24, no. 3 (2022): 851–923. <a href="https://doi.org/10.4171/jems/1103">https://doi.org/10.4171/jems/1103</a>.'
  ieee: 'Y. Guedes Bonthonneau and T. Weich, “Ruelle–Pollicott resonances for manifolds
    with hyperbolic cusps,” <i>Journal of the European Mathematical Society</i>, vol.
    24, no. 3, pp. 851–923, 2022, doi: <a href="https://doi.org/10.4171/jems/1103">10.4171/jems/1103</a>.'
  mla: Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances
    for Manifolds with Hyperbolic Cusps.” <i>Journal of the European Mathematical
    Society</i>, vol. 24, no. 3, European Mathematical Society - EMS - Publishing
    House GmbH, 2022, pp. 851–923, doi:<a href="https://doi.org/10.4171/jems/1103">10.4171/jems/1103</a>.
  short: Y. Guedes Bonthonneau, T. Weich, Journal of the European Mathematical Society
    24 (2022) 851–923.
date_created: 2023-01-05T16:23:34Z
date_updated: 2023-01-06T08:47:35Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: 10.4171/jems/1103
intvolume: '        24'
issue: '3'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
page: 851-923
publication: Journal of the European Mathematical Society
publication_identifier:
  issn:
  - 1435-9855
publication_status: published
publisher: European Mathematical Society - EMS - Publishing House GmbH
status: public
title: Ruelle–Pollicott resonances for manifolds with hyperbolic cusps
type: journal_article
user_id: '49178'
volume: 24
year: '2022'
...
---
_id: '34633'
article_number: '114118'
author:
- first_name: Kerstin
  full_name: Hesse, Kerstin
  id: '42608'
  last_name: Hesse
  orcid: 0000-0003-4125-1941
- first_name: Quoc Thong
  full_name: Le Gia, Quoc Thong
  last_name: Le Gia
citation:
  ama: Hesse K, Le Gia QT. L_2 error estimates for polynomial discrete penalized least-squares
    approximation on the sphere from noisy data. <i>Journal of Computational and Applied
    Mathematics</i>. 2022;408. doi:<a href="https://doi.org/10.1016/j.cam.2022.114118">10.1016/j.cam.2022.114118</a>
  apa: Hesse, K., &#38; Le Gia, Q. T. (2022). L_2 error estimates for polynomial discrete
    penalized least-squares approximation on the sphere from noisy data. <i>Journal
    of Computational and Applied Mathematics</i>, <i>408</i>, Article 114118. <a href="https://doi.org/10.1016/j.cam.2022.114118">https://doi.org/10.1016/j.cam.2022.114118</a>
  bibtex: '@article{Hesse_Le Gia_2022, title={L_2 error estimates for polynomial discrete
    penalized least-squares approximation on the sphere from noisy data}, volume={408},
    DOI={<a href="https://doi.org/10.1016/j.cam.2022.114118">10.1016/j.cam.2022.114118</a>},
    number={114118}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier
    BV}, author={Hesse, Kerstin and Le Gia, Quoc Thong}, year={2022} }'
  chicago: Hesse, Kerstin, and Quoc Thong Le Gia. “L_2 Error Estimates for Polynomial
    Discrete Penalized Least-Squares Approximation on the Sphere from Noisy Data.”
    <i>Journal of Computational and Applied Mathematics</i> 408 (2022). <a href="https://doi.org/10.1016/j.cam.2022.114118">https://doi.org/10.1016/j.cam.2022.114118</a>.
  ieee: 'K. Hesse and Q. T. Le Gia, “L_2 error estimates for polynomial discrete penalized
    least-squares approximation on the sphere from noisy data,” <i>Journal of Computational
    and Applied Mathematics</i>, vol. 408, Art. no. 114118, 2022, doi: <a href="https://doi.org/10.1016/j.cam.2022.114118">10.1016/j.cam.2022.114118</a>.'
  mla: Hesse, Kerstin, and Quoc Thong Le Gia. “L_2 Error Estimates for Polynomial
    Discrete Penalized Least-Squares Approximation on the Sphere from Noisy Data.”
    <i>Journal of Computational and Applied Mathematics</i>, vol. 408, 114118, Elsevier
    BV, 2022, doi:<a href="https://doi.org/10.1016/j.cam.2022.114118">10.1016/j.cam.2022.114118</a>.
  short: K. Hesse, Q.T. Le Gia, Journal of Computational and Applied Mathematics 408
    (2022).
date_created: 2022-12-20T17:37:16Z
date_updated: 2023-01-09T08:23:56Z
department:
- _id: '10'
doi: 10.1016/j.cam.2022.114118
intvolume: '       408'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
publication: Journal of Computational and Applied Mathematics
publication_identifier:
  issn:
  - 0377-0427
publication_status: published
publisher: Elsevier BV
status: public
title: L_2 error estimates for polynomial discrete penalized least-squares approximation
  on the sphere from noisy data
type: journal_article
user_id: '14931'
volume: 408
year: '2022'
...