Boundary of subdifferentials and calmness moduli in linear semi-infinite optimization

被引:0
作者
M. J. Cánovas
A. Hantoute
J. Parra
F. J. Toledo
机构
[1] Miguel Hernández University of Elche,Center of Operations Research
[2] Universidad de Chile,Departamento de Ingeniería Matemático, Centro de Modelamiento Matemático (CMM)
来源
Optimization Letters | 2015年 / 9卷
关键词
Variational analysis; Calmness; Semi-infinite programming; Linear programming;
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中图分类号
学科分类号
摘要
This paper was originally motivated by the problem of providing a point-based formula (only involving the nominal data, and not data in a neighborhood) for estimating the calmness modulus of the optimal set mapping in linear semi-infinite optimization under perturbations of all coefficients. With this aim in mind, the paper establishes as a key tool a basic result on finite-valued convex functions in the n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}-dimensional Euclidean space. Specifically, this result provides an upper limit characterization of the boundary of the subdifferential of such a convex function. When applied to the supremum function associated with our constraint system, this characterization allows us to derive an upper estimate for the aimed calmness modulus in linear semi-infinite optimization under the uniqueness of nominal optimal solution.
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页码:513 / 521
页数:8
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