A Generalization of Hoffman’s Lemma in Banach Spaces and Applications

A generalized version of an important theorem called Hoffman’s lemma in the book by Bonnans and Shapiro (Perturbation analysis of optimization problems, Springer, Berlin, 2000), which deals with generalized polyhedral convex multifunctions, is obtained in this paper. Under a mild assumption, the res...

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Bibliographic Details
Published in:Applied mathematics & optimization Vol. 91; no. 2; p. 40
Main Authors: Huy, Nguyen Quang, Tuan, Hoang Ngoc, Yen, Nguyen Dong
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2025
Springer Nature B.V
Subjects:
Algorithms
Applied mathematics
Banach spaces
Calculus of Variations and Optimal Control; Optimization
Control
Hilbert space
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimization
Perturbation methods
Quadratic programming
Simulation
Systems Theory
Theorems
Theoretical
Local error bound
90C20
Hoffman’s lemma in Banach spaces
Generalized affine variational inequality
49J53
Feasible descent method
49J40
Lipschitz continuity of a multifunction
Generalized polyhedral convex multifunction
Generalized quadratic programming problem
49M99
ISSN:0095-4616, 1432-0606
Online Access:Get full text
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Summary:A generalized version of an important theorem called Hoffman’s lemma in the book by Bonnans and Shapiro (Perturbation analysis of optimization problems, Springer, Berlin, 2000), which deals with generalized polyhedral convex multifunctions, is obtained in this paper. Under a mild assumption, the result allows us to demonstrate that the domain of a generalized polyhedral convex multifunction is closed and the multifunction is Lipschitz continuous on its effective domain. As concrete applications of the results, we prove some local error bounds for generalized affine variational inequalities and a theorem on the (strong) convergence of feasible descent methods for solving generalized quadratic programming problems.
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content type line 14
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-025-10238-6