Calmness of partially perturbed linear systems with an application to the central path

M. J. Cánovas, James Hall, M. A. Lopez, J. Parra

Research output: Contribution to journalArticlepeer-review


In this paper we develop point-based formulas for the calmness modulus of the feasible set mapping in the context of linear inequality systems with a fixed abstract constraint and (partially) perturbed linear constraints. The case of totally perturbed linear systems was previously analyzed in [9, Section 5]. We point out that the presence of such an abstract constraint yields the current paper to appeal to a notable different methodology with respect to previous works on the calmness modulus in linear programming. The interest of this model comes from the fact that partially perturbed systems naturally appear in many applications. As an illustration, the paper includes an example related to the classical central path construction. In this example we consider a certain feasible set mapping whose calmness modulus provides a measure of the convergence of the central path. Finally, we underline the fact that the expression for the calmness modulus obtained in this paper is (conceptually) implementable as far as it only involves the nominal data.
Original languageEnglish
Pages (from-to)465
Number of pages483
Issue number2-3
Early online date21 Sep 2018
Publication statusPublished - Mar 2019


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