College of Sciences, Chongqing Jiaotong Unversity ; College of Mathematics and Science, Chongqing University

Abstract: In locally convex Hausdorff topological vector spaces, ε-strongly efficient solutions for vector optimization with set-valued maps are discussed. Firstly, ε-strongly efficient point of set is introduced. Secondly, under the nearly cone-subconvex like set-valued maps, the theorem of scalarization for vector optimization is obtained. Finally, optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.

Key words: vector optimization, ε-strongly efficient point, nearly cone-subconvex like set-valued maps, ε-strongly efficient solutions, the theorem of scalarization, optimality conditions