---
_id: '51208'
abstract:
- lang: eng
text: AbstractApproximation of subdifferentials
is one of the main tasks when computing descent directions for nonsmooth optimization
problems. In this article, we propose a bisection method for weakly lower semismooth
functions which is able to compute new subgradients that improve a given approximation
in case a direction with insufficient descent was computed. Combined with a recently
proposed deterministic gradient sampling approach, this yields a deterministic
and provably convergent way to approximate subdifferentials for computing descent
directions.
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
citation:
ama: Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth
optimization. Computational Optimization and Applications. Published online
2024. doi:10.1007/s10589-024-00552-0
apa: Gebken, B. (2024). A note on the convergence of deterministic gradient sampling
in nonsmooth optimization. Computational Optimization and Applications.
https://doi.org/10.1007/s10589-024-00552-0
bibtex: '@article{Gebken_2024, title={A note on the convergence of deterministic
gradient sampling in nonsmooth optimization}, DOI={10.1007/s10589-024-00552-0},
journal={Computational Optimization and Applications}, publisher={Springer Science
and Business Media LLC}, author={Gebken, Bennet}, year={2024} }'
chicago: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
in Nonsmooth Optimization.” Computational Optimization and Applications,
2024. https://doi.org/10.1007/s10589-024-00552-0.
ieee: 'B. Gebken, “A note on the convergence of deterministic gradient sampling
in nonsmooth optimization,” Computational Optimization and Applications,
2024, doi: 10.1007/s10589-024-00552-0.'
mla: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
in Nonsmooth Optimization.” Computational Optimization and Applications,
Springer Science and Business Media LLC, 2024, doi:10.1007/s10589-024-00552-0.
short: B. Gebken, Computational Optimization and Applications (2024).
date_created: 2024-02-07T07:23:23Z
date_updated: 2024-02-08T08:05:54Z
department:
- _id: '101'
doi: 10.1007/s10589-024-00552-0
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
language:
- iso: eng
publication: Computational Optimization and Applications
publication_identifier:
issn:
- 0926-6003
- 1573-2894
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A note on the convergence of deterministic gradient sampling in nonsmooth optimization
type: journal_article
user_id: '32643'
year: '2024'
...
---
_id: '52726'
abstract:
- lang: eng
text: Heteroclinic structures organize global features of dynamical systems. We
analyse whether heteroclinic structures can arise in network dynamics with higher-order
interactions which describe the nonlinear interactions between three or more units.
We find that while commonly analysed model equations such as network dynamics
on undirected hypergraphs may be useful to describe local dynamics such as cluster
synchronization, they give rise to obstructions that allow to design of heteroclinic
structures in phase space. By contrast, directed hypergraphs break the homogeneity
and lead to vector fields that support heteroclinic structures.
article_type: original
author:
- first_name: Christian
full_name: Bick, Christian
last_name: Bick
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
citation:
ama: Bick C, von der Gracht S. Heteroclinic dynamics in network dynamical systems
with higher-order interactions. Journal of Complex Networks. 2024;12(2).
doi:10.1093/comnet/cnae009
apa: Bick, C., & von der Gracht, S. (2024). Heteroclinic dynamics in network
dynamical systems with higher-order interactions. Journal of Complex Networks,
12(2). https://doi.org/10.1093/comnet/cnae009
bibtex: '@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network
dynamical systems with higher-order interactions}, volume={12}, DOI={10.1093/comnet/cnae009},
number={2}, journal={Journal of Complex Networks}, publisher={Oxford University
Press (OUP)}, author={Bick, Christian and von der Gracht, Sören}, year={2024}
}'
chicago: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks
12, no. 2 (2024). https://doi.org/10.1093/comnet/cnae009.
ieee: 'C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical
systems with higher-order interactions,” Journal of Complex Networks, vol.
12, no. 2, 2024, doi: 10.1093/comnet/cnae009.'
mla: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks,
vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:10.1093/comnet/cnae009.
short: C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024).
date_created: 2024-03-22T09:04:57Z
date_updated: 2024-03-22T09:11:53Z
ddc:
- '510'
department:
- _id: '101'
doi: 10.1093/comnet/cnae009
external_id:
arxiv:
- '2309.02006'
file:
- access_level: closed
content_type: application/pdf
creator: svdg
date_created: 2024-03-22T09:06:07Z
date_updated: 2024-03-22T09:06:07Z
file_id: '52728'
file_name: heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf
file_size: 649155
relation: main_file
success: 1
file_date_updated: 2024-03-22T09:06:07Z
has_accepted_license: '1'
intvolume: ' 12'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
- Management Science and Operations Research
- Computer Networks and Communications
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf
oa: '1'
publication: Journal of Complex Networks
publication_identifier:
issn:
- 2051-1329
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Heteroclinic dynamics in network dynamical systems with higher-order interactions
type: journal_article
user_id: '97359'
volume: 12
year: '2024'
...
---
_id: '53317'
author:
- first_name: Youshan
full_name: Tao, Youshan
last_name: Tao
- first_name: Michael
full_name: Winkler, Michael
last_name: Winkler
citation:
ama: Tao Y, Winkler M. Global smooth solutions in a three-dimensional cross-diffusive
SIS epidemic model with saturated taxis at large densities. Evolution Equations
and Control Theory. 2023;12(6):1676-1687. doi:10.3934/eect.2023031
apa: Tao, Y., & Winkler, M. (2023). Global smooth solutions in a three-dimensional
cross-diffusive SIS epidemic model with saturated taxis at large densities. Evolution
Equations and Control Theory, 12(6), 1676–1687. https://doi.org/10.3934/eect.2023031
bibtex: '@article{Tao_Winkler_2023, title={Global smooth solutions in a three-dimensional
cross-diffusive SIS epidemic model with saturated taxis at large densities}, volume={12},
DOI={10.3934/eect.2023031},
number={6}, journal={Evolution Equations and Control Theory}, publisher={American
Institute of Mathematical Sciences (AIMS)}, author={Tao, Youshan and Winkler,
Michael}, year={2023}, pages={1676–1687} }'
chicago: 'Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Three-Dimensional
Cross-Diffusive SIS Epidemic Model with Saturated Taxis at Large Densities.” Evolution
Equations and Control Theory 12, no. 6 (2023): 1676–87. https://doi.org/10.3934/eect.2023031.'
ieee: 'Y. Tao and M. Winkler, “Global smooth solutions in a three-dimensional cross-diffusive
SIS epidemic model with saturated taxis at large densities,” Evolution Equations
and Control Theory, vol. 12, no. 6, pp. 1676–1687, 2023, doi: 10.3934/eect.2023031.'
mla: Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Three-Dimensional
Cross-Diffusive SIS Epidemic Model with Saturated Taxis at Large Densities.” Evolution
Equations and Control Theory, vol. 12, no. 6, American Institute of Mathematical
Sciences (AIMS), 2023, pp. 1676–87, doi:10.3934/eect.2023031.
short: Y. Tao, M. Winkler, Evolution Equations and Control Theory 12 (2023) 1676–1687.
date_created: 2024-04-07T12:30:25Z
date_updated: 2024-04-07T12:36:17Z
doi: 10.3934/eect.2023031
intvolume: ' 12'
issue: '6'
keyword:
- Applied Mathematics
- Control and Optimization
- Modeling and Simulation
language:
- iso: eng
page: 1676-1687
publication: Evolution Equations and Control Theory
publication_identifier:
issn:
- 2163-2480
publication_status: published
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic
model with saturated taxis at large densities
type: journal_article
user_id: '31496'
volume: 12
year: '2023'
...
---
_id: '30861'
abstract:
- lang: eng
text: AbstractWe 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 Fuller
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 turnpike property. This property
is further used in order to design simple and realistic suboptimal control strategies.
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. Journal of Optimization Theory
and Applications. Published online 2022. doi:10.1007/s10957-022-02023-0
apa: Caillau, J.-B., Djema, W., Gouzé, J.-L., Maslovskaya, S., & Pomet, J.-B.
(2022). Turnpike Property in Optimal Microbial Metabolite Production. Journal
of Optimization Theory and Applications. https://doi.org/10.1007/s10957-022-02023-0
bibtex: '@article{Caillau_Djema_Gouzé_Maslovskaya_Pomet_2022, title={Turnpike Property
in Optimal Microbial Metabolite Production}, DOI={10.1007/s10957-022-02023-0},
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.”
Journal of Optimization Theory and Applications, 2022. https://doi.org/10.1007/s10957-022-02023-0.
ieee: 'J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, and J.-B. Pomet, “Turnpike
Property in Optimal Microbial Metabolite Production,” Journal of Optimization
Theory and Applications, 2022, doi: 10.1007/s10957-022-02023-0.'
mla: Caillau, Jean-Baptiste, et al. “Turnpike Property in Optimal Microbial Metabolite
Production.” Journal of Optimization Theory and Applications, Springer
Science and Business Media LLC, 2022, doi:10.1007/s10957-022-02023-0.
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: '35206'
author:
- first_name: Bernard
full_name: Bonnard, Bernard
last_name: Bonnard
- first_name: Jérémy
full_name: Rouot, Jérémy
last_name: Rouot
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: Bonnard B, Rouot J, Wembe Moafo BE. Accessibility properties of abnormal geodesics
in optimal control illustrated by two case studies. Mathematical Control and
Related Fields. 2022;0(0):0-0. doi:10.3934/mcrf.2022052
apa: Bonnard, B., Rouot, J., & Wembe Moafo, B. E. (2022). Accessibility properties
of abnormal geodesics in optimal control illustrated by two case studies. Mathematical
Control and Related Fields, 0(0), 0–0. https://doi.org/10.3934/mcrf.2022052
bibtex: '@article{Bonnard_Rouot_Wembe Moafo_2022, title={Accessibility properties
of abnormal geodesics in optimal control illustrated by two case studies}, volume={0},
DOI={10.3934/mcrf.2022052},
number={0}, journal={Mathematical Control and Related Fields}, publisher={American
Institute of Mathematical Sciences (AIMS)}, author={Bonnard, Bernard and Rouot,
Jérémy and Wembe Moafo, Boris Edgar}, year={2022}, pages={0–0} }'
chicago: 'Bonnard, Bernard, Jérémy Rouot, and Boris Edgar Wembe Moafo. “Accessibility
Properties of Abnormal Geodesics in Optimal Control Illustrated by Two Case Studies.”
Mathematical Control and Related Fields 0, no. 0 (2022): 0–0. https://doi.org/10.3934/mcrf.2022052.'
ieee: 'B. Bonnard, J. Rouot, and B. E. Wembe Moafo, “Accessibility properties of
abnormal geodesics in optimal control illustrated by two case studies,” Mathematical
Control and Related Fields, vol. 0, no. 0, pp. 0–0, 2022, doi: 10.3934/mcrf.2022052.'
mla: Bonnard, Bernard, et al. “Accessibility Properties of Abnormal Geodesics in
Optimal Control Illustrated by Two Case Studies.” Mathematical Control and
Related Fields, vol. 0, no. 0, American Institute of Mathematical Sciences
(AIMS), 2022, pp. 0–0, doi:10.3934/mcrf.2022052.
short: B. Bonnard, J. Rouot, B.E. Wembe Moafo, Mathematical Control and Related
Fields 0 (2022) 0–0.
date_created: 2023-01-04T10:26:56Z
date_updated: 2023-01-16T12:07:51Z
doi: 10.3934/mcrf.2022052
issue: '0'
keyword:
- Applied Mathematics
- Control and Optimization
- General Medicine
language:
- iso: eng
page: 0-0
publication: Mathematical Control and Related Fields
publication_identifier:
issn:
- 2156-8472
- 2156-8499
publication_status: published
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: Accessibility properties of abnormal geodesics in optimal control illustrated
by two case studies
type: journal_article
user_id: '95394'
volume: '0'
year: '2022'
...
---
_id: '47961'
abstract:
- lang: eng
text: Due to failures or even the absence of an electricity grid, microgrid
systems are becoming popular solutions for electrifying African rural communities.
However, they are heavily stressed and complex to control due to their intermittency
and demand growth. Demand side management (DSM) serves as an option to increase
the level of flexibility on the demand side by scheduling users’ consumption patterns
profiles in response to supply. This paper proposes a demand-side management strategy
based on load shifting and peak clipping. The proposed approach was modelled in
a MATLAB/Simulink R2021a environment and was optimized using the artificial neural
network (ANN) algorithm. Simulations were carried out to test the model’s efficacy
in a stand-alone PV-battery microgrid in East Africa. The proposed algorithm reduces
the peak demand, smoothing the load profile to the desired level, and improves
the system’s peak to average ratio (PAR). The presence of deferrable loads has
been considered to bring more flexible demand-side management. Results promise
decreases in peak demand and peak to average ratio of about 31.2% and 7.5% through
peak clipping. In addition, load shifting promises more flexibility to customers.
article_number: '5215'
author:
- first_name: Godiana Hagile
full_name: Philipo, Godiana Hagile
id: '88505'
last_name: Philipo
- first_name: Josephine Nakato
full_name: Kakande, Josephine Nakato
id: '88649'
last_name: Kakande
- first_name: Stefan
full_name: Krauter, Stefan
id: '28836'
last_name: Krauter
orcid: 0000-0002-3594-260X
citation:
ama: Philipo GH, Kakande JN, Krauter S. Neural Network-Based Demand-Side Management
in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting and Peak-Clipping.
Energies. 2022;15(14). doi:10.3390/en15145215
apa: Philipo, G. H., Kakande, J. N., & Krauter, S. (2022). Neural Network-Based
Demand-Side Management in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting
and Peak-Clipping. Energies, 15(14), Article 5215. https://doi.org/10.3390/en15145215
bibtex: '@article{Philipo_Kakande_Krauter_2022, title={Neural Network-Based Demand-Side
Management in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting and
Peak-Clipping}, volume={15}, DOI={10.3390/en15145215},
number={145215}, journal={Energies}, publisher={MDPI AG}, author={Philipo, Godiana
Hagile and Kakande, Josephine Nakato and Krauter, Stefan}, year={2022} }'
chicago: Philipo, Godiana Hagile, Josephine Nakato Kakande, and Stefan Krauter.
“Neural Network-Based Demand-Side Management in a Stand-Alone Solar PV-Battery
Microgrid Using Load-Shifting and Peak-Clipping.” Energies 15, no. 14 (2022).
https://doi.org/10.3390/en15145215.
ieee: 'G. H. Philipo, J. N. Kakande, and S. Krauter, “Neural Network-Based Demand-Side
Management in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting and
Peak-Clipping,” Energies, vol. 15, no. 14, Art. no. 5215, 2022, doi: 10.3390/en15145215.'
mla: Philipo, Godiana Hagile, et al. “Neural Network-Based Demand-Side Management
in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting and Peak-Clipping.”
Energies, vol. 15, no. 14, 5215, MDPI AG, 2022, doi:10.3390/en15145215.
short: G.H. Philipo, J.N. Kakande, S. Krauter, Energies 15 (2022).
date_created: 2023-10-11T08:13:13Z
date_updated: 2024-10-17T08:46:23Z
department:
- _id: '53'
doi: 10.3390/en15145215
intvolume: ' 15'
issue: '14'
keyword:
- Energy (miscellaneous)
- Energy Engineering and Power Technology
- Renewable Energy
- Sustainability and the Environment
- Electrical and Electronic Engineering
- Control and Optimization
- Engineering (miscellaneous)
- Building and Construction
language:
- iso: eng
publication: Energies
publication_identifier:
issn:
- 1996-1073
publication_status: published
publisher: MDPI AG
status: public
title: Neural Network-Based Demand-Side Management in a Stand-Alone Solar PV-Battery
Microgrid Using Load-Shifting and Peak-Clipping
type: journal_article
user_id: '16148'
volume: 15
year: '2022'
...
---
_id: '33866'
abstract:
- lang: eng
text: Helhmoltz–Kirchhoff equations of motions of vortices of an incompressible
fluid in the plane define a dynamics with singularities and this leads to a Zermelo
navigation problem describing the ship travel in such a field where the control
is the heading angle. Considering one vortex, we define a time minimization problem
which can be analyzed with the technics of geometric optimal control combined
with numerical simulations, the geometric frame being the extension of Randers
metrics in the punctured plane, with rotational symmetry. Candidates as minimizers
are parameterized thanks to the Pontryagin Maximum Principle as extremal solutions
of a Hamiltonian vector field. We analyze the time minimal solution to transfer
the ship between two points where during the transfer the ship can be either in
a strong current region in the vicinity of the vortex or in a weak current region.
The analysis is based on a micro-local classification of the extremals using mainly
the integrability properties of the dynamics due to the rotational symmetry. The
discussion is complex and related to the existence of an isolated extremal (Reeb)
circle due to the vortex singularity. The explicit computation of cut points where
the extremal curves cease to be optimal is given and the spheres are described
in the case where at the initial point the current is weak.
article_number: S10
author:
- first_name: Bernard
full_name: Bonnard, Bernard
last_name: Bonnard
- first_name: Olivier
full_name: Cots, Olivier
last_name: Cots
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: 'Bonnard B, Cots O, Wembe Moafo BE. A Zermelo navigation problem with a vortex
singularity. ESAIM: Control, Optimisation and Calculus of Variations. 2020;27.
doi:10.1051/cocv/2020058'
apa: 'Bonnard, B., Cots, O., & Wembe Moafo, B. E. (2020). A Zermelo navigation
problem with a vortex singularity. ESAIM: Control, Optimisation and Calculus
of Variations, 27, Article S10. https://doi.org/10.1051/cocv/2020058'
bibtex: '@article{Bonnard_Cots_Wembe Moafo_2020, title={A Zermelo navigation problem
with a vortex singularity}, volume={27}, DOI={10.1051/cocv/2020058},
number={S10}, journal={ESAIM: Control, Optimisation and Calculus of Variations},
publisher={EDP Sciences}, author={Bonnard, Bernard and Cots, Olivier and Wembe
Moafo, Boris Edgar}, year={2020} }'
chicago: 'Bonnard, Bernard, Olivier Cots, and Boris Edgar Wembe Moafo. “A Zermelo
Navigation Problem with a Vortex Singularity.” ESAIM: Control, Optimisation
and Calculus of Variations 27 (2020). https://doi.org/10.1051/cocv/2020058.'
ieee: 'B. Bonnard, O. Cots, and B. E. Wembe Moafo, “A Zermelo navigation problem
with a vortex singularity,” ESAIM: Control, Optimisation and Calculus of Variations,
vol. 27, Art. no. S10, 2020, doi: 10.1051/cocv/2020058.'
mla: 'Bonnard, Bernard, et al. “A Zermelo Navigation Problem with a Vortex Singularity.”
ESAIM: Control, Optimisation and Calculus of Variations, vol. 27, S10,
EDP Sciences, 2020, doi:10.1051/cocv/2020058.'
short: 'B. Bonnard, O. Cots, B.E. Wembe Moafo, ESAIM: Control, Optimisation and
Calculus of Variations 27 (2020).'
date_created: 2022-10-24T12:51:05Z
date_updated: 2023-01-16T12:09:22Z
doi: 10.1051/cocv/2020058
intvolume: ' 27'
keyword:
- Computational Mathematics
- Control and Optimization
- Control and Systems Engineering
language:
- iso: eng
publication: 'ESAIM: Control, Optimisation and Calculus of Variations'
publication_identifier:
issn:
- 1292-8119
- 1262-3377
publication_status: published
publisher: EDP Sciences
status: public
title: A Zermelo navigation problem with a vortex singularity
type: journal_article
user_id: '95394'
volume: 27
year: '2020'
...