Well-Posedness of Set Optimization Problems with Set Order Defined by Minkowski Difference

Zhiang Zhou (), Kehao Feng () and Qamrul Hasan Ansari ()
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Zhiang Zhou: Chongqing University of Technology
Kehao Feng: Chongqing University of Technology
Qamrul Hasan Ansari: Chongqing University of Technology

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 2, No 16, 24 pages

Abstract: Abstract In this paper, we consider set optimization problems whose solution concepts are defined by means of set less order relations involving Minkwoski difference. We propose well-posedness and generalized well-posedness for set optimization problems, and derive sufficient and necessary conditions for these well-posedness. A relation between well-posedness and generalized well-posedness for set optimization problems is also given. We use a nonlinear scalarization method to establish necessary and sufficient conditions for the well-posedness and generalized well-posedness of set optimization problems. Several examples are given to illustrate our results.

Keywords: Set optimization problems; Set order relations; Well-posedness; Scalarization; 49J53; 49K40; 90C31 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02608-5

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