CLOSEDNESS OF THE OPTIMAL SOLUTION SETS FOR GENERAL VECTOR ALPHA OPTIMIZATION PROBLEMS

TRAN VAN  SU; DINH DIEU  HANG

CLOSEDNESS OF THE OPTIMAL SOLUTION SETS FOR GENERAL VECTOR ALPHA OPTIMIZATION PROBLEMS

Authors

TRAN VAN SU Department of Mathematics, Quang Nam University, 102 Hung Vuong, Tamky, Vietnam
DINH DIEU HANG Department of Basic Sciences, Thai Nguyen University of Information and Communication Technology, Thai Nguyen, Vietnam

Keywords:

Dual and primal general vector alpha optimization problems, Optimal solution sets, Upper C-continuous set-valued mapping, Hausdorff locally convex topological vector spaces

Abstract

The aim of paper is to study the closedness of the optimal solution sets for general vector alpha optimization problems in Hausdorff locally convex topological vector spaces. Firstly, we present the relationships between the optimal solution sets of primal and dual general vector alpha optimization problems. Secondly, making use of the upper semicontinuity of a set-valued mapping, we discuss the results on closedness of the optimal solution sets for general vector alpha optimization problems in infinite dimensional spaces.