Tightly Proper Efficiency in Vector Optimization with Nearly Cone-Subconvexlike Set-Valued Maps

Abstract

A scalarization theorem and two Lagrange multiplier theorems are established for tightly proper efficiency in vector optimization involving nearly cone-subconvexlike set-valued maps. A dual is proposed, and some duality results are obtained in terms of tightly properly efficient solutions. A new type of saddle point, which is called tightly proper saddle point of an appropriate set-valued Lagrange map, is introduced and is used to characterize tightly proper efficiency.

On the Sub Convexlike Optimization Problems

“…And, Jeyakumar defined X+subconvexlike function in [2]. There are plenty of research articles discussing subconvexlike optimization problems, e.g., see [4][5][6][7][8][9][10][11][12]. In this paper, we show that the sub convexlikeness introduced in [1] and the subconvexlikeness in [2] are actually equivalent in locally convex topological spaces (including normed linear spaces).…”

On Sub Convexlike Optimization Problems

“…Jeyakumar [2] introduced the definition of X + -sub convexlike function and defined X + -subconvexlike function in [3]. There are many research articles discussing subconvexlike optimization problems, e.g., see [4][5][6][7][8]. In this paper, by using partial order relations and the absorbing property of bounded convex sets in locally convex topological spaces [9], we proved that the sub convexlikeness introduced in [2] and subconvexlikeness in [3] are equivalent in locally convex topological spaces (including normed linear spaces).…”