Calmness modulus of fully perturbed linear programs

• 成果类型: Article
• 署名作者: Canovas, M. J.; Hantoute, A.; Parra, J.; Toledo, F. J.
• 署名单位: Universidad Miguel Hernandez de Elche; Universidad de Chile
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0926-x
• 发表日期: 2016
• 页码: 267-290
• 关键词: convex semiinfinite optimization; complementarity constraints; mathematical programs; metric regularity; convergence properties; banach-spaces; error-bounds; STABILITY; systems; MULTIFUNCTIONS

摘要

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 two applications related to algorithms traced out from the literature: the first one to a descent method in LP, and the second to a regularization method for linear programs with complementarity constraints.