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Calmness of linear programs under perturbations of all data: characterization and modulus

M.J. Cánovas (canovas***at***umh.es)
A. Hantoute (ahantoute***at***dim.uchile.cl)
J. Parra (parra***at***umh.es)
F.J. Toledo (javier.toledo***at***umh.es)

Abstract: This paper provides operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating the calmness modulus of the optimal set (argmin) mapping in linear optimization under uniqueness of nominal optimal solutions. Our analysis is developed in two different parametric settings. First, in the framework of canonical perturbations (i.e., perturbations of the objective function and the right-hand-side of the constraints), the paper provides a computationally tractable formula for the calmness modulus, which goes beyond some preliminary results of the literature. Second, in the framework of perturbations of all coefficients, the paper provides a characterization of the calmness property for the optimal set mapping, as well as an operative upper bound for the corresponding calmness modulus. Illustrative examples are provided.

Keywords: Variational analysis, Calmness, Linear programming, Calmness modulus

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Complementarity and Variational Inequalities

Citation: Authors 1,3,4: Center of Operations Research, Miguel Hernández University of Elche, 03202 Elche --- Author 2: Departamento de Ingeniería Matemática, Centro de Modelamiento Matemático(CMM), Universidad de Chile, Santiago, Chile --- Date: June, 2014

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Entry Submitted: 05/26/2014
Entry Accepted: 05/26/2014
Entry Last Modified: 06/18/2014

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