@article{30861,
  abstract     = {{<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       = {{Caillau, Jean-Baptiste and Djema, Walid and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}},
  issn         = {{0022-3239}},
  journal      = {{Journal of Optimization Theory and Applications}},
  keywords     = {{Applied Mathematics, Management Science and Operations Research, Control and Optimization}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Turnpike Property in Optimal Microbial Metabolite Production}}},
  doi          = {{10.1007/s10957-022-02023-0}},
  year         = {{2022}},
}

@article{45640,
  abstract     = {{I study a dynamic variant of the Dixit–Stiglitz (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       = {{Hoof, Simon}},
  issn         = {{1573-2878}},
  journal      = {{Journal of Optimization Theory and Applications}},
  number       = {{2}},
  publisher    = {{Springer}},
  title        = {{{Dynamic Monopolistic Competition}}},
  volume       = {{189}},
  year         = {{2021}},
}

@article{54166,
  author       = {{Khanjani Shiraz, Rashed and Tavana, Madjid and Di Caprio, Debora and Fukuyama, Hirofumi}},
  issn         = {{0022-3239}},
  journal      = {{Journal of Optimization Theory and Applications}},
  number       = {{1}},
  pages        = {{243--265}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions}}},
  doi          = {{10.1007/s10957-015-0857-y}},
  volume       = {{170}},
  year         = {{2016}},
}

@article{16612,
  author       = {{Grüne, L. and Junge, O.}},
  issn         = {{0022-3239}},
  journal      = {{Journal of Optimization Theory and Applications}},
  pages        = {{411--429}},
  title        = {{{Global Optimal Control of Perturbed Systems}}},
  doi          = {{10.1007/s10957-007-9312-z}},
  year         = {{2007}},
}

@article{16684,
  author       = {{Dellnitz, M. and Sch�tze, O. and Hestermeyer, T.}},
  issn         = {{0022-3239}},
  journal      = {{Journal of Optimization Theory and Applications}},
  pages        = {{113--136}},
  title        = {{{Covering Pareto Sets by Multilevel Subdivision Techniques}}},
  doi          = {{10.1007/s10957-004-6468-7}},
  year         = {{2005}},
}