Scalarization of $$\epsilon $$ ϵ -Super Efficient Solutions of Set-Valued Optimization Problems in Real Ordered Linear Spaces

Zhi-Ang Zhou () and Xin-Min Yang ()
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Zhi-Ang Zhou: College of Mathematics and Statistics, Chongqing University of Technology
Xin-Min Yang: School of Mathematics, Chongqing Normal University

Journal of Optimization Theory and Applications, 2014, vol. 162, issue 2, No 19, 680-693

Abstract: Abstract In this paper, we investigate the scalarization of $$\epsilon $$ ϵ -super efficient solutions of set-valued optimization problems in real ordered linear spaces. First, in real ordered linear spaces, under the assumption of generalized cone subconvexlikeness of set-valued maps, a dual decomposition theorem is established in the sense of $$\epsilon $$ ϵ -super efficiency. Second, as an application of the dual decomposition theorem, a linear scalarization theorem is given. Finally, without any convexity assumption, a nonlinear scalarization theorem characterized by the seminorm is obtained.

Keywords: Set-valued maps; Generalized cone subconvexlikeness; $$\epsilon $$ ϵ -Super efficient solutions; Scalarization; 90C26; 90C29; 90C30 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-014-0565-z

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