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

Authors

  • XIAOLING LIU Department of Mathematics, Hanshan Normal University, Chaozhou, 521041 China
  • DEHUI YUAN Department of Mathematics, Hanshan Normal University, Chaozhou, 521041 China
  • SHENGYUN YANG Department of Mathematics, Hanshan Normal University, Chaozhou, 521041 China
  • GUOMING LAI Department of Mathematics, Hanshan Normal University, Chaozhou, 521041 China

Keywords:

(G,α)-invexity, Kuhn-Tucker constraint qualification, (weakly) efficient solution, G-Kuhn-Tucker necessary optimality conditions

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.

Additional Files

Published

12/21/2011

Issue

Vol. 2 No. 2 (2011): JNAO

Section

Research Articles

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Copyright (c) 2010 Journal of Nonlinear Analysis and Optimization: Theory & Applications

Creative Commons License

This work is licensed under aย Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.