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

Z. A. Zhou () and J. W. Peng ()
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Z. A. Zhou: Chongqing University of Technology
J. W. Peng: Chongqing Normal University

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 3, No 6, 830-841

Abstract: 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 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.

Keywords: Set-valued map; Generalized cone subconvexlikeness; ϵ-Weakly efficient solution; ϵ-Global properly efficient solution; Scalarization (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-012-0045-2

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