A study of mixed discrete bilevel programs using semidefinite and semi-infinite programming |
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Institution: | 1. Department of Mathematics, Higher Training College, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon;2. AIMS-Cameroon Research Center, P.O. Box 608, Crystal Gardens, Limbe, Cameroon;3. Department of Mathematics and Computer Science, TU Bergakademie Freiberg, Akademiestr. 6, 09596, Freiberg, Germany |
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Abstract: | 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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Keywords: | Bilevel programming Semidefinite programming Semi-infinite programming Solution algorithm |
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