On Well-Posedness for Perturbed Quasi-Equilibrium and Quasi-Optimization Problems

• Published in: Numerical functional analysis and optimization Vol. 42; no. 5; pp. 583 - 607
• Main Authors: Anh, Lam Quoc, Khanh, Phan Quoc, My Van, Dang Thi
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04.06.2021; Taylor & Francis Ltd
• Subjects: (unique) well-posedness; Asymptotically solving sequence; Equilibrium; measure of noncompactness; Optimization; Perturbation; quasi-equilibrium problem; quasi-optimization problem; quasi-optimization problem with equilibrium constraints; Well posed problems
• ISSN: 0163-0563; 1532-2467
• DOI: 10.1080/01630563.2021.1901116

We propose definitions of well-posedness under perturbation in terms of suitable asymptotically solving sequences, not embedding a given problem into a parameterized family. When considering in detail quasi-equilibrium and quasi-optimization problems as well as optimization problems with equilibrium constraints, we establish sufficient conditions for both well-posedness and unique well-posedness. For cases with noncompact underlying sets of constraints, measures of noncompactness are employed. We provide numerous examples to ensure the essentialness of the assumptions imposed in the obtained results.