A characterization of generalized Levitin–Polyak well-posedness for parametric symmetric strong vector quasi-equilibrium problems and its application

Hung N. V., Duy N. H. V., Keller A. A., YAO J.

Optimization, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2026
  • Doi Number: 10.1080/02331934.2026.2653843
  • Journal Name: Optimization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, MathSciNet, zbMATH
  • Keywords: Levitin–Polyak well-posedness, Levitin–Polyak well-posedness in the generalized sense, Symmetric strong vector quasi-equilibrium problems, symmetric strong vector quasi-variational inequality problems
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

This paper aims to investigate the Levitin–Polyak (LP)-well-posedness of parametric symmetric strong vector quasi-equilibrium problems. Firstly, we consider symmetric strong vector quasi-equilibrium problems under perturbations. Secondly, we study the concept of upper semicontinuity in the setting of variable conic structures for vector-valued mappings and explore their properties. Thirdly, we establish the LP-well-posedness and generalized LP-well-posedness for these problems under appropriate conditions. Furthermore, employing the Hausdorff measure to assess non-compactness, we investigate the metric characterization of generalized LP-well-posedness for parametric symmetric strong vector quasi-equilibrium problems. As a final application, we delve into the LP-well-posedness of symmetric strong vector quasi-variational inequality problems. The results in this paper are novel and enhance several key findings in the existing literature. To illustrate these results, we present multiple examples.