Theorems of the Alternative for Multivalued Mappings and Applications to Mixed ConvexConcave Systems of Inequalities |
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Authors: | Michel Volle |
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Affiliation: | 1. Faculté des Sciences, Département de Mathématiques, Université d’Avignon, 33 rue Louis Pasteur, 84000, Avignon, France
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Abstract: | We provide a purely algebraic theorem of the alternative (and its topological variant) involving multivalued mappings under relaxed convexity assumptions. Various more or less classical applications are given, specially for nonconvex quadratic systems. In the second part of the paper we introduce an alternative formulation for a mixed convexconcave statement. The theory is applied to systems of mixed convexconcave inequalities. |
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