On vector matrix game and symmetric dual vector optimization problem

Fixexd point theory and applications

Jeong Min Hong¹  Gue Myung Lee¹  Moon Hee Kim² 

[1] Department of Applied Mathematics, Pukyong National University, Busan, Korea;School of Free Major, Tongmyong University, Busan, Korea

关键词: Symmetric Matrix;    Linear Programming Problem;    Probability Vector;    Vector Solution;    Vector Optimization Problem;   

DOI  :  10.1186/1687-1812-2012-233

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

A vector matrix game with more than two skew symmetric matrices, which is an extension of the matrix game, is defined and the symmetric dual problem for a nonlinear vector optimization problem is considered. Using the Kakutani fixed point theorem, we prove an existence theorem for a vector matrix game. We establish equivalent relations between the symmetric dual problem and its related vector matrix game. Moreover, we give an example illustrating the equivalent relations.

【 授权许可】

CC BY