Scalarization of Set-Valued Optimization Problems with Generalized Cone Subconvexlikeness in Real Ordered Linear Spaces

In real ordered linear spaces, an equivalent characterization of generalized cone subconvexlikeness of set-valued maps is firstly established. Secondly, under the assumption of generalized cone subconvexlikeness of set-valued maps, a scalarization theorem of set-valued optimization problems in the sense of ϵ-weak efficiency is obtained. Finally, by a scalarization approach, an existence theorem of ϵ-global properly efficient element of set-valued optimization problems is obtained. The results in this paper generalize and improve some known results in the literature.