danДоклады Национальной академии наук БеларусиDoklady of the National Academy of Sciences of Belarus1561-83232524-2431The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-8323-2019-63-5-526-532dan-658Research ArticleМАТЕМАТИКАMATHEMATICSО частичной устойчивости задач двухуровневого программирования с задачей нижнего уровня, линейной по основной переменнойOn partial calmness for bilevel programming problems with lower-level problem linear in lower-level variableМинченкоЛ. И.MinchenkoLeonid I.

Минченко Леонид Иванович - доктор физико-математических наук, профессор.

Ул. П. Бровки, 6, 220013, Минск

Minchenko Leonid Ivanovich - D. Sc. (Physics and Mathematics), Professor.

6, P. Brovka Str., 220013, Minsk

inform@bsuir.byСироткоС. И.SirotkoSergey I.

Сиротко Сергей Иванович - кандидат физико-математических наук, доцент.

Ул. П. Бровки, 6, 220013, Минск

Sirotko Sergey Ivanovich - Ph. D. (Physics and Mathematics), Assosiate professor.

sergeyis@bsuir.byБелорусский государственный университет информатики и радиоэлектроникиБеларусьBelarusian State University of Informatics and RadioelectronicsBelarus201906112019635526532Copyright © Минченко Л.И., Сиротко С.И., 20192019Минченко Л.И., Сиротко С.И.Minchenko L.I., Sirotko S.I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.belnauka.by/jour/article/view/658

Представлено членом-корреспондентом В. В. Гороховиком

Рассматриваются свойства обобщенной липшицевости множества решений задачи нижнего уровня в двухуровневой оптимизации. На их основе доказываются достаточные условия частичной устойчивости задач с линейной по основной переменной задачей нижнего уровня.

Communicated by Corresponding Member Valentine V. Gorokhovik

In the paper the Lipschitz-like properties of solution mapping of lower-level problems for bilevel programs are studied and sufficient conditions for partial calmness are proved on the basis of these properties.

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