Minimax problems for set-valued mappings with set optimization

Yu Zhang; Tao Chen

doi:10.3934/naco.2014.4.327

Article Contents

2014, Volume 4, Issue 4: 327-340. Doi: 10.3934/naco.2014.4.327

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Minimax problems for set-valued mappings with set optimization

Yu Zhang^1, and
Tao Chen^2,

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

Received: September 2014

Revised: December 2014

Published: December 2014

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Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 49J35, 49K35; Secondary: 90C47.

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