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.