Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (3): 593-602.

• Articles • Previous Articles     Next Articles

Optimality Conditions for Approximate Solutions on Nonconvex Vector Equilibrium Problems in Asplund Spaces

 LONG Xian-Jun   

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 40006
  • Received:2012-09-18 Revised:2013-04-16 Online:2014-06-25 Published:2014-06-25
  • Supported by:

    国家自然科学基金(11001287, 71271226)、重庆市自然科学基金(CSTC 2010BB9254, CSTC 2012jjA00039)和重庆市教委科技研究项目(KJ100711)资助

Abstract:

The purpose of this paper is to study approximate solutions for the vector equilibrium problem in Asplund spaces without any convexity assumption. We obtain optimality conditions for εe-quasi weakly efficient solutions, εe-quasi Henig efficient solutions, εe-quasi globally efficient solutions and εe-quasi efficient solutions to vector equilibrium problems 
by the Mordukhovich subdifferential. As applications of our results, we derive some optimality conditions for nonconvex vector optimization problems.

Key words: Nonvector vector equilibrium problem, Approximate solution, Optimality condition, Mordukhovich subdifferential

CLC Number: 

  • 90C26
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