Услови оптималности за изопериметријске проблеме оптимизације са непрекидним временом : докторска дисертација Vicanović, Jelena, 1987- Marinković, Boban, 1970- Savić, Aleksandar, 1967- Jović, Aleksandar, 1970- Gajić, Borislav Формулисан је конвексан проблем максимизације са непрекидним временом и дати су неопходни услови оптималности у бесконачно димензионом случају... A convex continuous-time maximization problem is formulated and the necessaryoptimality conditions in the infinite-dimensional case are obtained. As a main tool forobtaining optimal conditions in this dissertation we use the new theorem of the alternative.Since there’s no a differentiability assumption, we perform a linearization of the problemusing subdifferentials. It is proved that the multiplier with the objective function won’t beequal to zero. It was also shown that if the linear and non-linear constraints are separated,with additional assumptions it can be guaranteed that the multiplier with non-linear constraintswill also be non-zero. In the following, an integral constraint is added to the original convexproblem, so that a Lyapunov-type problem, i.e. an isoperimetric problem, is considered. Linearizationof the problem using subdifferentials proved to be a practical way to ignore the lackof differentiability, so the optimality conditions were derived in a similar way. It is shown thatthe obtained results will also be valid for the vector case of the isoperimetric problem.Additionally, the optimality conditions for the smooth problem were considered. On theminimization problem, it was shown that the necessary conditions of Karush-Kuhn-Tucker typewill be valid with the additional regularity constraint condition. Also, any point that satisfiesthe mentioned optimality conditions will be a global minimum. Математика-Оптимизација / Mathematics -Оptimization Datum odbrane: 18.06.2024. 2024 62 стр. 2220263 bytes OSNO - Opšta sistematizacija naučnih oblasti, Operaciono istraživanje OSNO - Opšta sistematizacija naučnih oblasti, Operaciono istraživanje OSNO - Opšta sistematizacija naučnih oblasti, Računarsko programiranje. Aplikativni programi OSNO - Opšta sistematizacija naučnih oblasti, Računarsko programiranje. Aplikativni programi Проблеми оптимизације са непрекидним временом, Конвексно програмирање, Услови оптималности, Теореме алтернативе, Изопериметријски проблеми, Вишекритеријумски проблеми оптимизације са непрекидним временом Continuous-time programming, Convex programming, Optimality conditions, Theorems of the alternative, Isoperimetric problems, Multiobjective continuous-time programming problems http://creativecommons.org/licenses/by-nc-nd/3.0/at/legalcode https://phaidrabg.bg.ac.rs/o:38120 cobiss:188752905 thesis:10112 srp info:eu-repo/semantics/bachelorThesis