On the stability of infinite-dimensional linear inequality systems
作者:
M. A. López,
J. A. Mira,
G. Torregrosa,
期刊:
Numerical Functional Analysis and Optimization
(Taylor Available online 1998)
卷期:
Volume 19,
issue 9-10
页码: 1065-1077
ISSN:0163-0563
年代: 1998
DOI:10.1080/01630569808816874
出版商: Marcel Dekker, Inc.
关键词: Infinite linear optimization;perturbations;stability;solution set mapping;Primary 65F99;Primary 15A39;Secondary 49D39;Secondary 52A40
数据来源: Taylor
摘要:
The principal aim of this paper is to study the stability of the solution set mapping of a system composed by an arbitrary set of linear inequalities in an infinite-dimensional space. The unknowns space is assumed to be metrizable, which allows us to measure the size of any possible perturbation. Conditions guaranteeing the closedness, the lower semicontinuity and the upper semicontmuity of this mapping, at a particular nominal system, are given in the paper. The more significant differences with respect to the finite dimensional case, previously approached in the context of the so-called semi-infinite optimization, are illustrated by means of convenient examples.
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