OPTIMALITY CONDITIONS FOR (G, \alpha) INVEX MULTIOBJECTIVE PROGRAMMING

Authors

  • X. Liu Department of Mathematics, Hanshan Normal University, Chaozhou, 521041 China
  • D. Yuan Department of Mathematics, Hanshan Normal University, Chaozhou, 521041 China
  • S. Yang Department of Mathematics, Hanshan Normal University, Chaozhou, 521041 China
  • G. Lai Department of Mathematics, Hanshan Normal University, Chaozhou, 521041 China

Abstract

In this paper, a generalization of convexity, namely $(G, \alpha)$-invexity, is considered in the case of nonlinear multiobjective programming problems where the functions constituting vector optimization problems are differentiable. Two auxiliary programming problems are constructed to present the modified KuhnTucker necessary optimality conditions for (CVP). With the help of auxiliary programming problems (GCVP), the relation between (CVP) and (GCVP) is discussed; while with the help of ('GP), a new KuhnTucker necessary condition for (CVP) is presented. Furthermore, the sufficiency of the introduced G KarushKuhnTucker(GKuhnTucker) necessary optimality conditions, for nonconvex multiobjective programming problem involving $(G, \alpha)$-invex functions, is proved.

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Published

2011-12-21

How to Cite

Liu, X., Yuan, D., Yang, S., & Lai, G. (2011). OPTIMALITY CONDITIONS FOR (G, \alpha) INVEX MULTIOBJECTIVE PROGRAMMING. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 2(2), 305-315. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/62

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Section

Research Article