MINIMAX PROGRAMMING WITH $(G, \ALPHA)$-INVEXTY

Authors

  • X. Liu Department of Mathematics, Hanshan Normal University, Chaozhou, 521041 China
  • D. Yuan Department of Mathematics, Hanshan Normal University, Chaozhou, 521041 China
  • D. Qu Department of Mathematics, Hanshan Normal University, Chaozhou, 521041 China

Abstract

In this paper, we deal with the minimax programming (P) under the differentiable  $(G, \alpha)$-invexity which was proposed in [J. Nonlinear Anal. Optim. 2(2): 305-315]. With the help of auxiliary programming problem $(G-P)$, some new Kuhn-Tucker necessary conditions, namely for G-Kuhn-Tucker necessary conditions, is presented for the minimax programming (P). Also G-Karush-Kuhn-Tucker sufficient conditions under $(G, \alpha)$-invexity assumption are obtained for the minimax programming (P). Making use of these optimality conditions, we construct a dual problem (DI) for (P) and establish weak, strong and strict converse duality theorems between problems (P)and (DI).

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Published

2013-08-10

How to Cite

Liu, X., Yuan, D., & Qu, D. (2013). MINIMAX PROGRAMMING WITH $(G, \ALPHA)$-INVEXTY. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 4(2), 173-180. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/224

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Section

Research Article