Solution Stability and Well-Posedness for Classes of Parametric Set Optimization Problems

Zai-Yun Peng (), Yue Zeng (), Thai Doan Chuong (), Sangwoon Yun () and Xin Yang ()
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Zai-Yun Peng: Yunnan Normal University
Yue Zeng: Sichuan University
Thai Doan Chuong: Department of Mathematics, Brunel University of London
Sangwoon Yun: Sungkyunkwan University
Xin Yang: Chongqing JiaoTong University

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 17, 25 pages

Abstract: Abstract This paper investigates the solution stability and well-posedness for a parametric set optimization problem (PSOP), where lower and upper set order relations are induced by an improvement set. We provide new sufficient conditions for the outer-continuity, outer-openness and inner-openness of the solution mapping of (PSOP). By utilizing the property of cone-continuity, we derive sufficient conditions ensuring the Levitin-Polyak well-posedness for (PSOP) and the Hadamard well-posedness for a related parametric implicit set optimization problem (ISOP). Numerical examples are also given to illustrate the main results.

Keywords: Set optimization; Improvement set; Solution Stability; Levitin-Polyak well-posedness; Hadamard well-posedness; 49J53; 49K40; 90C31 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02850-x

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