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On Solving Bilevel Optimization Problems with a Nonconvex Lower Level: The Case of a Bimatrix Game

Авторы: Orlov A.V.

Журнал: Lecture Notes in Computer Science: 20th Intern. Conf. on Mathematical Optimization Theory and Operations Research, MOTOR 2021 (Irkutsk, 5-10 July 2021)

Том: 12755

Номер:

Год: 2021

Отчётный год: 2021

Издательство:

Местоположение издательства:

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DOI: 10.1007/978-3-030-77876-7_16

Аннотация: This paper addresses the optimistic statement of one class of bilevel optimization problems (BOPs) with a nonconvex lower level. Namely, we study BOPs with a convex quadratic objective function at the upper level and with a bimatrix game at the lower level. It is known that the problem of finding a Nash equilibrium point in a bimatrix game is equivalent to the special nonconvex optimization problem with a bilinear structure. Nevertheless, we can replace such a lower level with its optimality conditions and transform the original bilevel problem into a single-level nonconvex optimization problem. Then we apply the original Global Search Theory (GST) for general D.C. optimization problems and the Exact Penalization Theory to the resulting problem. After that, a special method of local search, which takes into account the structure of the problem under consideration, is developed.

Индексируется WOS: Q4

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Да

Индексируется ВАК: Нет

Индексируется CORE: Нет

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