Dominators for Multiple-objective Quasiconvex Maximization Problems |
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Authors: | EMILIO CARRIZOSA FRANK PLASTRIA |
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Institution: | (1) Facultad de Matematicas, Universidad de Sevilla, C/ Tarfia s / n, 41012 Sevilla, Spain;(2) Department of Management Informatics, Vrije Universiteit Brussel, Pleinlaan, 2, B- 1050 Brussels, Belgium |
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Abstract: | In this paper we address the problem of finding a dominator for a multiple-objective maximization problem with quasiconvex functions. The one-dimensional case is discussed in some detail, showing how a Branch-and-Bound procedure leads to a dominator with certain minimality properties. Then, the well-known result stating that the set of vertices of a polytope S contains an optimal solution for single-objective quasiconvex maximization problems is extended to multiple-objective problems, showing that, under upper-semicontinuity assumptions, the set of (k 21)-dimensional faces is a dominator for k-objective problems. In particular, for biobjective quasiconvex problems on a polytope S, the edges of S constitute a dominator, from which a dominator with minimality properties can be extracted by Branch-and Bound methods. |
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Keywords: | Multiple-objective problems Quasiconvex maximization Dominators |
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