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Solving Quasiconcave Bilevel Programming Problem
Department of Mathematics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
Department of Computer Sciences, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
- 1 Department of Mathematics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
- 2 Department of Computer Sciences, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
American Journal of Operations Research·Volume 07 (2017)·Pages 121–132·Published 14 March 2017·DOI10.4236/ajor.2017.72009
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Abstract
In this paper, we find the solution of a quasiconcave bilevel programming problem (QCBPP). After formulating a Bilevel Multiobjective Programming Problem (BMPP), we characterize its leader objective function and its feasible set. We show some necessary and sufficient conditions to establish a convex union of set of efficient point, an efficient set at the QCBPP. Based on this result, we formulate and solve a new QCBPP. Finally, we illustrate our approach with a numerical example.
KeywordsBilevel Multiobjective Programming ProblemQuasiconcave Bilevel Programming ProblemEfficient Set
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