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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The authors wish to thank the anonymous referees for their valuable critical comments which have definitely improved the first version of the manuscript.
Funding
This research has been partially supported by Grant PGC2018-097960-B-C21 from MICINN, Spain, and ERDF, “A way to make Europe”, European Union.
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Dedicated to R.T. Rockafellar on his 85th birthday
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Argáez, C., Cánovas, M. & Parra, J. Calmness of Linear Constraint Systems under Structured Perturbations with an Application to the Path-Following Scheme. Set-Valued Var. Anal 29, 839–860 (2021). https://doi.org/10.1007/s11228-021-00597-x
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DOI: https://doi.org/10.1007/s11228-021-00597-x
Keywords
- Calmness
- Linear systems of equalities and inequalities
- Primal-dual path-following algorithm
- Linear programming
- Feasible set mapping