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

• Published in: Journal of global optimization Vol. 57; no. 4; pp. 1359 - 1373
• Main Authors: Zhang, Y., Li, S. J.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.12.2013; Springer; Springer Nature B.V
• Subjects: Computer Science; Control theory; Equilibrium; Game theory; Inequality; Mapping; Mathematical analysis; Mathematical functions; Mathematics; Mathematics and Statistics; Maximization; Minimax technique; Neighborhoods; Operations Research/Decision Theory; Optimization; Real Functions; Scalars; Studies; Theorems; Vector space; Vectors (mathematics); 49J35; Minimax theorem; Set-valued mapping; 90C47; Vector optimization; Cone saddle point; 49K35

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 gen...