Author:
Hong Jeong Min,Kim Moon Hee,Lee Gue Myung
Abstract
Abstract
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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Geometry and Topology
Reference11 articles.
1. Cowles Commission Monograph 13;GB Dantzig,1951
2. Chandra S, Craven BD, Mond B: Nonlinear programming duality and matrix game equivalence. J. Aust. Math. Soc. Ser. B, Appl. Math 1985, 26: 422–429. 10.1017/S033427000000463X
3. Chandra S, Mond B, Duraga Prasad MV: Continuous linear programs and continuous matrix game equivalence. In Recent Developments in Mathematical Programming. Edited by: Kumar S. Gordan and Breach Science Publishers, New York; 1991:397–406.
4. Kim DS, Noh K: Symmetric dual nonlinear programming and matrix game equivalence. J. Math. Anal. Appl. 2004, 298: 1–13. 10.1016/j.jmaa.2003.12.049
5. Preda V: On nonlinear programming and matrix game equivalence. J. Aust. Math. Soc. Ser. B, Appl. Math 1994, 35: 429–438. 10.1017/S0334270000009528