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A study of mixed discrete bilevel programs using semidefinite and semi-infinite programming

Floriane Mefo Kue,Stephan Dempe

Operations Research Letters(2023)

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摘要
In this paper, we study the bilevel programming problem with discrete polynomial lower level problem. We start by transforming the problem into a bilevel problem comprising a semidefinite program (SDP for short) in the lower level problem. Then, we are able to deduce some conditions of existence of solutions for the original problem. After that, we again change the bilevel problem with SDP in the lower level problem into a semi-infinite program. With the aid of the exchange technique, for simple bilevel programs, an algorithm for computing a global optimal solution is suggested, the convergence is shown, and a numerical example is given.
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关键词
Bilevel programming,Semidefinite programming,Semi-infinite programming,Solution algorithm
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