Convergence of Solutions in Set Optimization Based on Null Set

C. S. Lalitha () and Anveksha Moar ()
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C. S. Lalitha: University of Delhi South Campus
Anveksha Moar: University of Delhi

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 21, 27 pages

Abstract: Abstract The main objective of the paper is to study the convergence of solution sets in set optimization where the set order relation is based on the concept of null set. The perturbed problems involve perturbation of both the objective map and the feasible set. Upper and lower Painlevé–Kuratowski convergence results are established for the minimal and weak minimal solution sets in the domain space. Additionally, a new notion of convergence is defined in terms of the scalarizing function in the hyperspace to establish a convergence in the image space.

Keywords: Set optimization; Scalarization; Null set; Painlevé–Kuratowski convergence; Semi-continuity; 90C31; 49J53 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02852-9

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