On Well-Posedness for Perturbed Quasi-Equilibrium and Quasi-Optimization Problems. (4th June 2021)

• Record Type: Journal Article
• Authors: Anh, Lam Quoc; Khanh, Phan Quoc; My Van, Dang Thi
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 5(2021)
• Page Start: 583
• Page End: 607
• Publication Date: 2021-06-04
• Subjects: Asymptotically solving sequence -- measure of noncompactness -- quasi-equilibrium problem -- quasi-optimization problem -- quasi-optimization problem with equilibrium constraints -- (unique) well-posedness; 49K40 -- 90C31 -- 65K99; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1901116
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: 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.