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

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Título: Calmness of partially perturbed linear systems with an application to the central path
Autor/es: Cánovas Cánovas, María Josefa | Hall, Julian A.J. | López Cerdá, Marco A. | Parra López, Juan
Grupo/s de investigación o GITE: Laboratorio de Optimización (LOPT)
Centro, Departamento o Servicio: Universidad de Alicante. Departamento de Matemáticas
Palabras clave: Calmness | Local error bounds | Linear programming | Feasible set mapping | Interior point methods
Área/s de conocimiento: Estadística e Investigación Operativa
Fecha de publicación: 21-sep-2018
Editor: Taylor & Francis
Cita bibliográfica: Optimization. 2018. doi:10.1080/02331934.2018.1523403
Resumen: 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 [Cánovas MJ, López MA, Parra J, et al. Calmness of the feasible set mapping for linear inequality systems. Set-Valued Var Anal. 2014;22:375–389, 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.
Patrocinador/es: This research has been partially supported by Grant MTM2014-59179-C2-(1,2)-P from MINECO, Spain, and FEDER ‘Una manera de hacer Europa’, European Union.
URI: http://hdl.handle.net/10045/81530
ISSN: 0233-1934 (Print) | 1029-4945 (Online)
DOI: 10.1080/02331934.2018.1523403
Idioma: eng
Tipo: info:eu-repo/semantics/article
Derechos: © 2018 Informa UK Limited, trading as Taylor & Francis Group
Revisión científica: si
Versión del editor: https://doi.org/10.1080/02331934.2018.1523403
Aparece en las colecciones:INV - LOPT - Artículos de Revistas

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