Scalarization of set-valued optimization problems with generalized cone subconvexlikeness in real ordered linear spaces
Autors' abstract: 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 \(\epsilon \)-weak efficiency is obtained. Finally, by a scalarization approach, an existence theorem of \(\epsilon \)-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.
scientific article; zbMATH DE number 6135497
scientific article