mathnasТруды Института математики НАН БеларусиProceedings of the Institute of Mathematics of the NAS of Belarus1812-5093Институт математики НАН Беларуси10.67268/1812-5093-2026-34-1s-32-49VEVQUFmathnas-183Research ArticleДИСКРЕТНАЯ МАТЕМАТИКА И МАТЕМАТИЧЕСКАЯ КИБЕРНЕТИКАDISCRETE MATHEMATICS AND MATHEMATICAL CYBERNETICSПараметрические задачи полубесконечного программирования: свойства функций решенийParametric semi-infinite programming problems: properties of solution functionsКостюковаО. И.KostyukovaO. I.

Минск

kostyukova@im.bas-net.byЧемисоваТ. В.TchemisovaT. V.

Факультет математики, Университетский кампус Сантьяго, Авейру

Department of Mathematics, Campus Universitario Santiago, Aveiro

tatiana@ua.ptИнститут математики НАН БеларусиBelarusУниверситет АвейруПортугалияUniversity of AveiroPortugal202607112026341s3249Copyright © Костюкова О.И., Чемисова Т.В., 20262026Костюкова О.И., Чемисова Т.В.Kostyukova O.I., Tchemisova T.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://mathnas.ejournal.by/jour/article/view/183

В работе исследуются анализ чувствительности и асимптотическое поведение решений параметрических выпуклых задач полубесконечного программирования с компактными полиэдральными индексными множествами. Анализируются свойства оптимальных решений, множителей Лагранжа и множества активных индексов при стремлении параметра к номинальному значению. При стандартных предположениях о гладкости, выпуклости и выполнении условий регулярности ограничений получены соотношения, характеризующие пределы и производные первого порядка соответствующих прямых и двойственных функций решений.

We study sensitivity and asymptotic behavior of solutions to parametric convex semi-infinite programming problems with compact polyhedral index sets. We analyze properties of optimal solutions, Lagrange multipliers, and active sets as the parameter approaches a nominal value. Under standard smoothness, convexity, and constraint qualification assumptions, we characterize the limits and first-order derivatives of the associated primal and dual mappings.

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The authors declare that there are no conflicts of interest present.