Operations Research Transactions ›› 2012, Vol. 16 ›› Issue (3): 75-83.

• Original Articles • Previous Articles     Next Articles

Characterization of solution sets of E-convex programming problems

JIANG Gen1, LIU Xuewen1, WANG Gang1, CHEN Lin1   

  1. 1. Department of Mathematics, Chongqing Normal University
  • Received:2010-12-17 Revised:2012-02-28 Online:2012-09-15 Published:2012-09-18
  • Contact: LIU Xuewen

Abstract: In this paper, an important class of generalized convex programming problems, E-convex program, was considered. We defined the E-Gateaux differential of E-convex function on the E-convex set,  and got some characteristic theorems  of the E-Gateaux differential of E-convex function, proposed the equivalent characterizations of the solution sets of E-convex programming problems by using the characteristic theorems. For an E-convex program in a normed vector space with the objective function admitting the E-Gateaux differential at an optimal solution, we showed that the solution set consists of the feasible points lying in the hyperplane whose normal vector equals the E-Gateaux differential.

Key words: E-gateaux differential, characterization of solution sets, E-convex function, E-convex program, sub-differential

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