Scalarizations and Optimality of Constrained Set-Valued Optimization Using Improvement Sets and Image Space Analysis

Zhiang Zhou (), Wang Chen () and Xinmin Yang ()
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Zhiang Zhou: Chongqing University of Technology
Wang Chen: Sichuan University
Xinmin Yang: Chongqing Normal University

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 3, No 8, 944-962

Abstract: Abstract In this paper, we aim at applying improvement sets and image space analysis to investigate scalarizations and optimality conditions of the constrained set-valued optimization problem. Firstly, we use the improvement set to introduce a new class of generalized convex set-valued maps. Secondly, under suitable assumptions, some scalarization results of the constrained set-valued optimization problem are obtained in the sense of (weak) optimal solution characterized by the improvement set. Finally, by considering two classes of nonlinear separation functions, we present the separation between two suitable sets in image space and derive some optimality conditions for the constrained set-valued optimization problem. It shows that the existence of a nonlinear separation is equivalent to a saddle point condition of the generalized Lagrangian set-valued functions.

Keywords: Image space analysis; Set-valued maps; Improvement set; Scalarization; Optimality; 90C26; 90C29; 90C46; 26B25 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-019-01554-3

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