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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Vydáno v:Set-valued and variational analysis Ročník 29; číslo 4; s. 839 - 860
Hlavní autoři: Argáez, C., Cánovas, M.J., Parra, J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.12.2021
Springer Nature B.V
Témata:
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
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-021-00597-x