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Sharp estimates for approximate and exact solutions to quasi-optimization problems.
- Source :
-
Optimization . May2022, Vol. 71 Issue 5, p1331-1355. 25p. - Publication Year :
- 2022
-
Abstract
- In this paper, we consider a special implicit set-valued map representing solutions to a parametric quasi-optimization problem, (Q O p t) for short. This model finds its motivation in quasi-convex programming and generalized Nash equilibria modelled by the supremum of the so-called Nikaido–Isoda functions. We exploit a new recent variant of the celebrated Lim's Lemma considered in the context of metric regularity and approximate fixed points to establish quantitative stability for ε-approximate solutions to (Q O p t) under parametric perturbations in the spirit of the result presented for convex programming in the seminal contribution by Attouch and Wets [Quantitative stability of variational systems: III. ε-approximatesolutions. Math Program. 1993;61:197–214, Theorem 4.3]. Sharp estimates are then extended to parametric exact solutions to (Q O p t) by means of a qualitative stability analysis stressing the role of Painlevé-Kuratowski and Pompeiu-Hausdorff convergence for sets of approximate minima to a set of exact ones under usual compactness and/or completeness conditions. Finally, we apply our main result to a non-smooth mathematical program under polyhedral convex mappings and situate our contribution in the close recent literature. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02331934
- Volume :
- 71
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 157269418
- Full Text :
- https://doi.org/10.1080/02331934.2021.1873986