[{"keyword":["Applied Mathematics","Management Science and Operations Research","Control and Optimization"],"language":[{"iso":"eng"}],"_id":"30861","user_id":"87909","department":[{"_id":"636"}],"abstract":[{"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>","lang":"eng"}],"status":"public","type":"journal_article","publication":"Journal of Optimization Theory and Applications","title":"Turnpike Property in Optimal Microbial Metabolite Production","doi":"10.1007/s10957-022-02023-0","publisher":"Springer Science and Business Media LLC","date_updated":"2022-04-08T18:23:02Z","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","last_name":"Gouzé","full_name":"Gouzé, Jean-Luc"},{"last_name":"Maslovskaya","id":"87909","full_name":"Maslovskaya, Sofya","first_name":"Sofya"},{"first_name":"Jean-Baptiste","full_name":"Pomet, Jean-Baptiste","last_name":"Pomet"}],"date_created":"2022-04-08T17:23:13Z","year":"2022","citation":{"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} }","short":"J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, J.-B. Pomet, Journal of Optimization Theory and Applications (2022).","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>.","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>","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>","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>."},"publication_status":"published","publication_identifier":{"issn":["0022-3239","1573-2878"]}},{"intvolume":"       170","page":"243-265","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>","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>.","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>.","short":"R. Khanjani Shiraz, M. Tavana, D. Di Caprio, H. Fukuyama, Journal of Optimization Theory and Applications 170 (2016) 243–265.","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>.","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} }","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>"},"year":"2016","issue":"1","publication_identifier":{"issn":["0022-3239","1573-2878"]},"publication_status":"published","doi":"10.1007/s10957-015-0857-y","title":"Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions","volume":170,"author":[{"last_name":"Khanjani Shiraz","full_name":"Khanjani Shiraz, Rashed","first_name":"Rashed"},{"first_name":"Madjid","id":"31858","full_name":"Tavana, Madjid","last_name":"Tavana"},{"first_name":"Debora","full_name":"Di Caprio, Debora","last_name":"Di Caprio"},{"last_name":"Fukuyama","full_name":"Fukuyama, Hirofumi","first_name":"Hirofumi"}],"date_created":"2024-05-11T11:25:18Z","publisher":"Springer Science and Business Media LLC","date_updated":"2024-05-11T11:52:17Z","status":"public","publication":"Journal of Optimization Theory and Applications","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"277"}],"user_id":"51811","_id":"54166"},{"date_updated":"2022-01-06T06:52:53Z","author":[{"first_name":"L.","last_name":"Grüne","full_name":"Grüne, L."},{"last_name":"Junge","full_name":"Junge, O.","first_name":"O."}],"date_created":"2020-04-16T08:03:02Z","title":"Global Optimal Control of Perturbed Systems","doi":"10.1007/s10957-007-9312-z","publication_identifier":{"issn":["0022-3239","1573-2878"]},"publication_status":"published","year":"2007","page":"411-429","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>","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>.","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} }","short":"L. Grüne, O. Junge, Journal of Optimization Theory and Applications (2007) 411–429.","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>"},"_id":"16612","department":[{"_id":"101"}],"user_id":"15701","language":[{"iso":"eng"}],"publication":"Journal of Optimization Theory and Applications","type":"journal_article","status":"public"},{"status":"public","type":"journal_article","publication":"Journal of Optimization Theory and Applications","language":[{"iso":"eng"}],"_id":"16684","user_id":"15701","department":[{"_id":"101"}],"year":"2005","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>","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.","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>.","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>.","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} }","short":"M. Dellnitz, O. Sch�tze, T. Hestermeyer, Journal of Optimization Theory and Applications (2005) 113–136.","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>"},"page":"113-136","publication_status":"published","publication_identifier":{"issn":["0022-3239","1573-2878"]},"title":"Covering Pareto Sets by Multilevel Subdivision Techniques","doi":"10.1007/s10957-004-6468-7","date_updated":"2022-01-06T06:52:54Z","author":[{"full_name":"Dellnitz, M.","last_name":"Dellnitz","first_name":"M."},{"full_name":"Sch�tze, O.","last_name":"Sch�tze","first_name":"O."},{"first_name":"T.","full_name":"Hestermeyer, T.","last_name":"Hestermeyer"}],"date_created":"2020-04-16T10:31:32Z"}]