Metrically Levitin–Polyak well-posed parametric set optimization problem

Biswajit Tahu (), Mansi Dhingra () and Pankaj Kumar Garg ()
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Biswajit Tahu: University of Delhi
Mansi Dhingra: University of Delhi
Pankaj Kumar Garg: University of Delhi

OPSEARCH, 2025, vol. 62, issue 1, No 11, 249-267

Abstract: Abstract In this article, concepts of metrically pointwise and metrically global Levitin–Polyak (LP) well-posed parametric set optimization problems are introduced. Characterizations of metrically pointwise and metrically global LP well-posed parametric set optimization problems are scrutinized in detail. Connections between metrically pointwise LP well-posed parametric set optimization problems and a approximate solution map are established. Connections between metrically global LP well-posed parametric set optimization problems and the approximate solution map are also established. The role of upper semicontinuity and compactness of the approximate solution map are also analysed for a parametric set optimization problem to be metrically pointwise and global LP well-posed. The role of excess function in the approximate solution map is also scrutinized for a parametric set optimization problem to be metrically pointwise LP well-posed. Relationships between pointwise LP well-posedness and metrically pointwise LP well-posedness are derived. Relationships between global LP well-poseness and metrically global LP well-posedness are also analysed. All the links are properly established to prove the necessary and sufficient conditions.

Keywords: Parametric set optimization problem; $$\alpha $$ α -weak minimal solution; Levitin–Polyak well-posedness; Excess functions; Hausdorff distance; 49J53; 90C26; 90C46; 90C31 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s12597-024-00761-5

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