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

Y. Zhang () and Shuanming Li

Journal of Global Optimization, 2013, vol. 57, issue 4, 1359-1373

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. Copyright Springer Science+Business Media New York 2013

Keywords: Minimax theorem; Cone saddle point; Vector optimization; Set-valued mapping; 49J35; 49K35; 90C47 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-9992-2

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