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Metrically Levitin–Polyak well-posed parametric set optimization problem

Author

Listed:
  • Biswajit Tahu

    (University of Delhi)

  • Mansi Dhingra

    (University of Delhi)

  • Pankaj Kumar Garg

    (University of Delhi)

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.

Suggested Citation

  • Biswajit Tahu & Mansi Dhingra & Pankaj Kumar Garg, 2025. "Metrically Levitin–Polyak well-posed parametric set optimization problem," OPSEARCH, Springer;Operational Research Society of India, vol. 62(1), pages 249-267, March.
    • Handle: RePEc:spr:opsear:v:62:y:2025:i:1:d:10.1007_s12597-024-00761-5
    DOI: 10.1007/s12597-024-00761-5
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    References listed on IDEAS

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    1. G. P. Crespi & A. Guerraggio & M. Rocca, 2007. "Well Posedness in Vector Optimization Problems and Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 213-226, January.
    2. Y. D. Xu & S. J. Li, 2016. "On the solution continuity of parametric set optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 223-237, August.
    3. Qamrul Hasan Ansari & Andreas H Hamel & Pradeep Kumar Sharma, 2020. "Ekeland’s variational principle with weighted set order relations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 117-136, February.
    4. E. Miglierina & E. Molho & M. Rocca, 2005. "Well-Posedness and Scalarization in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 391-409, August.
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