Scalarization of Set-Valued Optimization Problems with Generalized Cone Subconvexlikeness in Real Ordered Linear Spaces |
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Authors: | Z A Zhou J W Peng |
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Institution: | 1.Department of Applied Mathematics,Chongqing University of Technology,Chongqing,China;2.School of Mathematics,Chongqing Normal University,Chongqing,China |
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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 ?-weak efficiency is obtained. Finally, by a scalarization approach, an existence theorem of ?-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. |
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