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<p>In this paper, we introduce two types of Levitin-Polyak well-posedness for split quasi-equilibrium problems. We establish different characterizations of these well-posedness notions with and without gap functions for split quasi-equilibrium problems. Furthermore, we provide equivalence between the well-posedness of constrained optimization problems and that of split quasi-equilibrium problems using gap function techniques. By analyzing the upper semicontinuity of approximate solution sets, we derive necessary and/or sufficient conditions for type I Levitin-Polyak well-posedness. Numerical examples are provided to validate our theoretical findings.</p>

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Levitin–Polyak well-posedness of split quasi-equilibrium problems

  • 期刊论文

  • 发表日期：

    2026年1月27日

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  • Kanchan Mittal,
  • Bin Pang,
  • Jen-Chih Yao

摘要

In this paper, we introduce two types of Levitin-Polyak well-posedness for split quasi-equilibrium problems. We establish different characterizations of these well-posedness notions with and without gap functions for split quasi-equilibrium problems. Furthermore, we provide equivalence between the well-posedness of constrained optimization problems and that of split quasi-equilibrium problems using gap function techniques. By analyzing the upper semicontinuity of approximate solution sets, we derive necessary and/or sufficient conditions for type I Levitin-Polyak well-posedness. Numerical examples are provided to validate our theoretical findings.