Scalarization of $$\epsilon $$ ϵ -Super Efficient Solutions of Set-Valued Optimization Problems in Real Ordered Linear Spaces

Abstract

In this paper, we investigate the scalarization of $$\epsilon $$ ∈ -super efficient solutions of set-valued optimization problems in real ordered linear spaces. First, in real ordered linear spaces, under the assumption of generalized cone subconvexlikeness of set-valued maps, a dual decomposition theorem is established in the sense of $$\epsilon $$ ∈ -super efficiency. Second, as an application of the dual decomposition theorem, a linear scalarization theorem is given. Finally, without any convexity assumption, a nonlinear scalarization theorem characterized by the seminorm is obtained.