Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.10.2026.4.03

Volume 10, Issue 4, 1 August 2026, Pages 753-777

 

Abstract. In this paper, we aim to elaborate on some notions of Levitin-Polyak well-posedness for set optimization problems with a variable set structure and well-posedness of the corresponding scalar optimization problem by employing a nonlinear scalarization function. We categorize these notions into two classes including pointwise and global Levitin–Polyak well-posedness. Some necessary and sufficient conditions for these well-posedness are established. Additionally, we characterize LP well-posedness for set optimization problems in terms of the upper Hausdorff convergence and Painlevé-Kuratowski convergence of approximate solution sets. Furthermore, we explore the interrelationships among these well-posedness concepts. Finally, we explore some applications of the obtained results to multi-criteria traffic network equilibrium problems.

 

How to Cite this Article:
W. Wang, Y. Xu, Levitin-Polyak well-posedness for set optimization with a variable set structure, J. Nonlinear Var. Anal. 10 (2026), 753-777.