Optimality conditions for continuous-time isoperimetric optimization problems

[Ј. Вицановић]

62 стр.

Математика-Оптимизација / Mathematics -Оptimization

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 necessary optimality conditions in the infinite-dimensional case are obtained. As a main tool for obtaining 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 problem using subdifferentials. It is proved that the multiplier with the objective function won’t be equal 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 constraints will also be non-zero. In the following, an integral constraint is added to the original convex problem, so that a Lyapunov-type problem, i.e. an isoperimetric problem, is considered. Linearization of the problem using subdifferentials proved to be a practical way to ignore the lack of differentiability, so the optimality conditions were derived in a similar way. It is shown that the 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 the minimization problem, it was shown that the necessary conditions of Karush-Kuhn-Tucker type will be valid with the additional regularity constraint condition. Also, any point that satisfies the mentioned optimality conditions will be a global minimum.

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

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