Approximate weak efficiency of the set-valued optimization problem with variable ordering structures

Zhiang Zhou (), Wenbin Wei (), Fei Huang () and Kequan Zhao ()
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Zhiang Zhou: Chongqing University of Technology
Wenbin Wei: Chongqing Normal University
Fei Huang: Chongqing University of Technology
Kequan Zhao: Chongqing Normal University

Journal of Combinatorial Optimization, 2024, vol. 48, issue 3, No 12, 13 pages

Abstract: Abstract In locally convex spaces, we introduce the new notion of approximate weakly efficient solution of the set-valued optimization problem with variable ordering structures (in short, SVOPVOS) and compare it with other kinds of solutions. Under the assumption of near $$\mathcal {D}(\cdot )$$ D ( · ) -subconvexlikeness, we establish linear scalarization theorems of (SVOPVOS) in the sense of approximate weak efficiency. Finally, without any convexity, we obtain a nonlinear scalarization theorem of (SVOPVOS). We also present some examples to illustrate our results.

Keywords: Set-valued maps; Variable ordering structures; Approximate weakly efficient solution; Scalarization; 90C26; 90C29; 90C46; 26B25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-024-01211-0

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