Calmness modulus of fully perturbed linear programs
Author
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 full perturbations
(perturbations of all coefficients), after characterizing the calmness property
for the optimal set mapping, the paper provides an operative upper bound for the
corresponding calmness modulus, as well as some illustrative examples. We provide
Patrocinador
MINECO Spain, Fondecyt, ECOS-Conicyt, Math-Amsud
Indexation
Artículo de publicación ISI
Identifier
URI: https://repositorio.uchile.cl/handle/2250/141353
DOI: 10.1007/s10107-015-0926-x
ISSN: 0025-5610
Quote Item
Math. Program., Ser. A (2016) 158:267–290
Collections
The following license files are associated with this item: