Lipschitz-Like Property for Linear Constraint Systems

In this paper, we consider a linear constraint system with a set constraint. We investigate the Lipschitz-like property of such systems with an explicit set constraint under full perturbations (including the matrix perturbation) and derive some sufficient and necessary conditions for this property....

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 199; no. 3; pp. 1281 - 1296
Main Authors: Yao, Wenfang, Yang, Xiaoqi
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2023
Springer Nature B.V
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Constraints
Engineering
Euclidean space
Inequality
Lipschitz condition
Mathematical functions
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Perturbation
Theory of Computation
Linear systems
Lipschitz-like property
Linear portfolio selection
49J53
93C05
91B28
90C05
Coderivatives
60K10
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:In this paper, we consider a linear constraint system with a set constraint. We investigate the Lipschitz-like property of such systems with an explicit set constraint under full perturbations (including the matrix perturbation) and derive some sufficient and necessary conditions for this property. We also make use of some other approaches like outer-subdifferentials and error bounds to characterize such a property. We later apply the obtained results to linear portfolio selection problems with different settings and obtain some sufficient conditions for the parametric feasible set mapping to enjoy the Lipschitz-like property with various stock selection constraints.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-023-02300-6