Minimax theorems for scalar set-valued mappings with nonconvex domains and applications

Authors:
Y. Zhang;S. J. Li
Affiliations:
College of Mathematics and Statistics, Chongqing University, Chongqing, China 401331;College of Mathematics and Statistics, Chongqing University, Chongqing, China 401331
Venue:
Journal of Global Optimization
Year:
2013

Citing 11
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Abstract

In this paper, by virtue of the separation theorem of convex sets, we prove a minimax theorem, a cone saddle point theorem and a Ky Fan minimax theorem for a scalar set-valued mapping under nonconvex assumptions of its domains, respectively. As applications, we obtain an existence result for the generalized vector equilibrium problem with a set-valued mapping. Simultaneously, we also obtain some generalized Ky Fan minimax theorems for set-valued mappings, in which the minimization and the maximization of set-valued mappings are taken in the sense of vector optimization.