---
_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: '45640'
abstract:
- lang: eng
  text: "I study a dynamic variant of the Dixitâ\x80\x93Stiglitz (Am Econ Rev 67(3),
    1977) model of monopolistic competition by introducing price stickiness à la
    Fershtman and Kamien (Econometrica 55(5), 1987). The analysis is restricted to
    bounded quantity and price paths that fulfill the necessary conditions for an
    open-loop Nash equilibrium. I show that there exists a symmetric steady state
    and that its stability depends on the degree of product differentiation. When
    moving from complements to perfect substitutes, the steady state is either a locally
    asymptotically unstable (spiral) source, a stable (spiral) sink or a saddle point.
    I further apply the Hopf bifurcation theorem and prove the existence of limit
    cycles, when passing from a stable to an unstable steady state. Lastly, I provide
    a numerical example and show that there exists a stable limit cycle."
author:
- first_name: Simon
  full_name: Hoof, Simon
  last_name: Hoof
citation:
  ama: Hoof S. Dynamic Monopolistic Competition. <i>Journal of Optimization Theory
    and Applications</i>. 2021;189(2).
  apa: Hoof, S. (2021). Dynamic Monopolistic Competition. <i>Journal of Optimization
    Theory and Applications</i>, <i>189</i>(2).
  bibtex: '@article{Hoof_2021, title={Dynamic Monopolistic Competition}, volume={189},
    number={2}, journal={Journal of Optimization Theory and Applications}, publisher={Springer},
    author={Hoof, Simon}, year={2021} }'
  chicago: Hoof, Simon. “Dynamic Monopolistic Competition.” <i>Journal of Optimization
    Theory and Applications</i> 189, no. 2 (2021).
  ieee: S. Hoof, “Dynamic Monopolistic Competition,” <i>Journal of Optimization Theory
    and Applications</i>, vol. 189, no. 2, 2021.
  mla: Hoof, Simon. “Dynamic Monopolistic Competition.” <i>Journal of Optimization
    Theory and Applications</i>, vol. 189, no. 2, Springer, 2021.
  short: S. Hoof, Journal of Optimization Theory and Applications 189 (2021).
date_created: 2023-06-15T14:05:25Z
date_updated: 2023-07-05T07:23:54Z
department:
- _id: '205'
- _id: '475'
intvolume: '       189'
issue: '2'
language:
- iso: eng
project:
- _id: '7'
  grant_number: '160364472'
  name: 'SFB 901 - A3: SFB 901 - Der Markt für Services: Anreize, Algorithmen, Implementation
    (Subproject A3)'
- _id: '1'
  grant_number: '160364472'
  name: 'SFB 901: SFB 901: On-The-Fly Computing - Individualisierte IT-Dienstleistungen
    in dynamischen Märkten '
- _id: '2'
  name: 'SFB 901 - A: SFB 901 - Project Area A'
publication: Journal of Optimization Theory and Applications
publication_identifier:
  issn:
  - 1573-2878
publication_status: published
publisher: Springer
quality_controlled: '1'
status: public
title: Dynamic Monopolistic Competition
type: journal_article
user_id: '477'
volume: 189
year: '2021'
...
---
_id: '54166'
author:
- first_name: Rashed
  full_name: Khanjani Shiraz, Rashed
  last_name: Khanjani Shiraz
- first_name: Madjid
  full_name: Tavana, Madjid
  id: '31858'
  last_name: Tavana
- first_name: Debora
  full_name: Di Caprio, Debora
  last_name: Di Caprio
- first_name: Hirofumi
  full_name: Fukuyama, Hirofumi
  last_name: Fukuyama
citation:
  ama: Khanjani Shiraz R, Tavana M, Di Caprio D, Fukuyama H. Solving Geometric Programming
    Problems with Normal, Linear and Zigzag Uncertainty Distributions. <i>Journal
    of Optimization Theory and Applications</i>. 2016;170(1):243-265. doi:<a href="https://doi.org/10.1007/s10957-015-0857-y">10.1007/s10957-015-0857-y</a>
  apa: Khanjani Shiraz, R., Tavana, M., Di Caprio, D., &#38; Fukuyama, H. (2016).
    Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty
    Distributions. <i>Journal of Optimization Theory and Applications</i>, <i>170</i>(1),
    243–265. <a href="https://doi.org/10.1007/s10957-015-0857-y">https://doi.org/10.1007/s10957-015-0857-y</a>
  bibtex: '@article{Khanjani Shiraz_Tavana_Di Caprio_Fukuyama_2016, title={Solving
    Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions},
    volume={170}, DOI={<a href="https://doi.org/10.1007/s10957-015-0857-y">10.1007/s10957-015-0857-y</a>},
    number={1}, journal={Journal of Optimization Theory and Applications}, publisher={Springer
    Science and Business Media LLC}, author={Khanjani Shiraz, Rashed and Tavana, Madjid
    and Di Caprio, Debora and Fukuyama, Hirofumi}, year={2016}, pages={243–265} }'
  chicago: 'Khanjani Shiraz, Rashed, Madjid Tavana, Debora Di Caprio, and Hirofumi
    Fukuyama. “Solving Geometric Programming Problems with Normal, Linear and Zigzag
    Uncertainty Distributions.” <i>Journal of Optimization Theory and Applications</i>
    170, no. 1 (2016): 243–65. <a href="https://doi.org/10.1007/s10957-015-0857-y">https://doi.org/10.1007/s10957-015-0857-y</a>.'
  ieee: 'R. Khanjani Shiraz, M. Tavana, D. Di Caprio, and H. Fukuyama, “Solving Geometric
    Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions,”
    <i>Journal of Optimization Theory and Applications</i>, vol. 170, no. 1, pp. 243–265,
    2016, doi: <a href="https://doi.org/10.1007/s10957-015-0857-y">10.1007/s10957-015-0857-y</a>.'
  mla: Khanjani Shiraz, Rashed, et al. “Solving Geometric Programming Problems with
    Normal, Linear and Zigzag Uncertainty Distributions.” <i>Journal of Optimization
    Theory and Applications</i>, vol. 170, no. 1, Springer Science and Business Media
    LLC, 2016, pp. 243–65, doi:<a href="https://doi.org/10.1007/s10957-015-0857-y">10.1007/s10957-015-0857-y</a>.
  short: R. Khanjani Shiraz, M. Tavana, D. Di Caprio, H. Fukuyama, Journal of Optimization
    Theory and Applications 170 (2016) 243–265.
date_created: 2024-05-11T11:25:18Z
date_updated: 2024-05-11T11:52:17Z
department:
- _id: '277'
doi: 10.1007/s10957-015-0857-y
intvolume: '       170'
issue: '1'
language:
- iso: eng
page: 243-265
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: Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty
  Distributions
type: journal_article
user_id: '51811'
volume: 170
year: '2016'
...
---
_id: '16612'
author:
- first_name: L.
  full_name: Grüne, L.
  last_name: Grüne
- first_name: O.
  full_name: Junge, O.
  last_name: Junge
citation:
  ama: Grüne L, Junge O. Global Optimal Control of Perturbed Systems. <i>Journal of
    Optimization Theory and Applications</i>. 2007:411-429. doi:<a href="https://doi.org/10.1007/s10957-007-9312-z">10.1007/s10957-007-9312-z</a>
  apa: Grüne, L., &#38; Junge, O. (2007). Global Optimal Control of Perturbed Systems.
    <i>Journal of Optimization Theory and Applications</i>, 411–429. <a href="https://doi.org/10.1007/s10957-007-9312-z">https://doi.org/10.1007/s10957-007-9312-z</a>
  bibtex: '@article{Grüne_Junge_2007, title={Global Optimal Control of Perturbed Systems},
    DOI={<a href="https://doi.org/10.1007/s10957-007-9312-z">10.1007/s10957-007-9312-z</a>},
    journal={Journal of Optimization Theory and Applications}, author={Grüne, L. and
    Junge, O.}, year={2007}, pages={411–429} }'
  chicago: Grüne, L., and O. Junge. “Global Optimal Control of Perturbed Systems.”
    <i>Journal of Optimization Theory and Applications</i>, 2007, 411–29. <a href="https://doi.org/10.1007/s10957-007-9312-z">https://doi.org/10.1007/s10957-007-9312-z</a>.
  ieee: L. Grüne and O. Junge, “Global Optimal Control of Perturbed Systems,” <i>Journal
    of Optimization Theory and Applications</i>, pp. 411–429, 2007.
  mla: Grüne, L., and O. Junge. “Global Optimal Control of Perturbed Systems.” <i>Journal
    of Optimization Theory and Applications</i>, 2007, pp. 411–29, doi:<a href="https://doi.org/10.1007/s10957-007-9312-z">10.1007/s10957-007-9312-z</a>.
  short: L. Grüne, O. Junge, Journal of Optimization Theory and Applications (2007)
    411–429.
date_created: 2020-04-16T08:03:02Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1007/s10957-007-9312-z
language:
- iso: eng
page: 411-429
publication: Journal of Optimization Theory and Applications
publication_identifier:
  issn:
  - 0022-3239
  - 1573-2878
publication_status: published
status: public
title: Global Optimal Control of Perturbed Systems
type: journal_article
user_id: '15701'
year: '2007'
...
---
_id: '16684'
author:
- first_name: M.
  full_name: Dellnitz, M.
  last_name: Dellnitz
- first_name: O.
  full_name: Sch�tze, O.
  last_name: Sch�tze
- first_name: T.
  full_name: Hestermeyer, T.
  last_name: Hestermeyer
citation:
  ama: Dellnitz M, Sch�tze O, Hestermeyer T. Covering Pareto Sets by Multilevel Subdivision
    Techniques. <i>Journal of Optimization Theory and Applications</i>. 2005:113-136.
    doi:<a href="https://doi.org/10.1007/s10957-004-6468-7">10.1007/s10957-004-6468-7</a>
  apa: Dellnitz, M., Sch�tze, O., &#38; Hestermeyer, T. (2005). Covering Pareto Sets
    by Multilevel Subdivision Techniques. <i>Journal of Optimization Theory and Applications</i>,
    113–136. <a href="https://doi.org/10.1007/s10957-004-6468-7">https://doi.org/10.1007/s10957-004-6468-7</a>
  bibtex: '@article{Dellnitz_Sch�tze_Hestermeyer_2005, title={Covering Pareto Sets
    by Multilevel Subdivision Techniques}, DOI={<a href="https://doi.org/10.1007/s10957-004-6468-7">10.1007/s10957-004-6468-7</a>},
    journal={Journal of Optimization Theory and Applications}, author={Dellnitz, M.
    and Sch�tze, O. and Hestermeyer, T.}, year={2005}, pages={113–136} }'
  chicago: Dellnitz, M., O. Sch�tze, and T. Hestermeyer. “Covering Pareto Sets by
    Multilevel Subdivision Techniques.” <i>Journal of Optimization Theory and Applications</i>,
    2005, 113–36. <a href="https://doi.org/10.1007/s10957-004-6468-7">https://doi.org/10.1007/s10957-004-6468-7</a>.
  ieee: M. Dellnitz, O. Sch�tze, and T. Hestermeyer, “Covering Pareto Sets by Multilevel
    Subdivision Techniques,” <i>Journal of Optimization Theory and Applications</i>,
    pp. 113–136, 2005.
  mla: Dellnitz, M., et al. “Covering Pareto Sets by Multilevel Subdivision Techniques.”
    <i>Journal of Optimization Theory and Applications</i>, 2005, pp. 113–36, doi:<a
    href="https://doi.org/10.1007/s10957-004-6468-7">10.1007/s10957-004-6468-7</a>.
  short: M. Dellnitz, O. Sch�tze, T. Hestermeyer, Journal of Optimization Theory and
    Applications (2005) 113–136.
date_created: 2020-04-16T10:31:32Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/s10957-004-6468-7
language:
- iso: eng
page: 113-136
publication: Journal of Optimization Theory and Applications
publication_identifier:
  issn:
  - 0022-3239
  - 1573-2878
publication_status: published
status: public
title: Covering Pareto Sets by Multilevel Subdivision Techniques
type: journal_article
user_id: '15701'
year: '2005'
...