American Institute of Mathematical Sciences

2014, 4(4): 327-340. doi: 10.3934/naco.2014.4.327

Minimax problems for set-valued mappings with set optimization

 1 College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China 2 College of Public Foundation, Yunnan Open University, Kunming 650223, China

Received  September 2014 Revised  December 2014 Published  December 2014

In this paper, we introduce a class of set-valued mappings with some set order relations, which is called uniformly same-order. For this sort of mappings, we obtain some existence results of saddle points and depict the structures of the sets of saddle points. Moreover, we obtain a minimax theorem and establish an equivalent relationship between the minimax theorem and a saddle point theorem for the scalar set-valued mappings, in which the minimization and the maximization of set-valued mappings are taken in the sense of set optimization.
Citation: Yu Zhang, Tao Chen. Minimax problems for set-valued mappings with set optimization. Numerical Algebra, Control & Optimization, 2014, 4 (4) : 327-340. doi: 10.3934/naco.2014.4.327
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