Naslov (srp)

Услови оптималности за изопериметријске проблеме оптимизације са непрекидним временом : докторска дисертација

Autor

Vicanović, Jelena, 1987-

Doprinosi

Jović, Aleksandar, 1970-
Savić, Aleksandar, 1967-
Gajić, Borislav
Marinković, Boban, 1970-

Opis (eng)

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.

Opis (srp)

Формулисан је конвексан проблем максимизације са непрекидним временом и дати су неопходни услови оптималности у бесконачно димензионом случају...

Opis (srp)

Математика-Оптимизација / Mathematics -Оptimization Datum odbrane: 18.06.2024.

Jezik

srpski

Datum

2024

Licenca

Ovo delo je licencirano pod uslovima licence
Creative Commons CC BY-NC-ND 3.0 AT - Creative Commons Autorstvo - Nekomercijalno - Bez prerada 3.0 Austria License.

http://creativecommons.org/licenses/by-nc-nd/3.0/at/legalcode

Predmet

OSNO - Opšta sistematizacija naučnih oblasti, Operaciono istraživanje

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

OSNO - Opšta sistematizacija naučnih oblasti, Operaciono istraživanje

OSNO - Opšta sistematizacija naučnih oblasti, Računarsko programiranje. Aplikativni programi

Continuous-time programming, Convex programming, Optimality conditions, Theorems of the alternative, Isoperimetric problems, Multiobjective continuous-time programming problems