Calmness of Linear Constraint Systems under Structured Perturbations with an Application to the Path-Following Scheme

We are concerned with finite linear constraint systems in a parametric framework where the right-hand side is an affine function of the perturbation parameter. Such structured perturbations provide a unified framework for different parametric models in the literature, as block, directional and/or pa...

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Bibliographic Details
Published in:Set-valued and variational analysis Vol. 29; no. 4; pp. 839 - 860
Main Authors: Argáez, C., Cánovas, M.J., Parra, J.
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.12.2021
Springer Nature B.V
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Optimization
Perturbation
90C31
Feasible set mapping
90C51
49J53
Linear programming
90C05
Calmness
Linear systems of equalities and inequalities
Primal-dual path-following algorithm
ISSN:1877-0533, 1877-0541
Online Access:Get full text
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Summary:We are concerned with finite linear constraint systems in a parametric framework where the right-hand side is an affine function of the perturbation parameter. Such structured perturbations provide a unified framework for different parametric models in the literature, as block, directional and/or partial perturbations of both inequalities and equalities. We extend some recent results about calmness of the feasible set mapping and provide an application to the convergence of a certain path-following algorithmic scheme. We underline the fact that our formula for the calmness modulus depends only on the nominal data, which makes it computable in practice.
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ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-021-00597-x