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LEVITIN-POLYAK WELL-POSEDNESS FOR SET OPTIMIZATION WITH A VARIABLE SET STRUCTURE
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DOI：10.23952/jnva.10.2026.4.03.png)
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Abstract
En 中文
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 wellposedness for set optimization problems in terms of the upper Hausdorff convergence and Painleve- 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.
Keywords:
Levitin-Polyak well-posedness
Painleve-Kuratowski convergence
Set optimization
Upper Hausdorff convergence
Variable structure
Journal
IF:
1.9
Papers:
72
Citations:
356