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

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


Title: Calmness of Linear Constraint Systems under Structured Perturbations with an Application to the Path-Following Scheme
Author: Garcia, Carlos Argaez
Cánovas, M. J.
Parra, J.
Date: 2021-07-14
Language: English
Scope:
Department: Science Institute
Series: Set-Valued and Variational Analysis; ()
ISSN: 0927-6947
DOI: https://doi.org/10.1007/s11228-021-00597-x
Subject: Forritun; Calmness; Feasible set mapping; Linear programming; Linear systems of equalities and inequalities; Primal-dual path-following algorithm; Analysis; Statistics and Probability; Numerical Analysis; Geometry and Topology; Applied Mathematics
URI: https://hdl.handle.net/20.500.11815/2708

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Citation:

Garcia , C A , Cánovas , M J & Parra , J 2021 , ' Calmness of Linear Constraint Systems under Structured Perturbations with an Application to the Path-Following Scheme ' , Set-Valued and Variational Analysis . https://doi.org/10.1007/s11228-021-00597-x

Abstract:

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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Publisher Copyright: © 2021, The Author(s).

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