Hoffman's Error Bound, Local Controllability, and Sensitivity Analysis

Our aim is to present sufficient conditions ensuring Hoffman'serror bound for lower semicontinuous nonconvex inequality systems and to analyze its impact on the local controllability, implicit function theorem for (non-Lipschitz) multivalued mappings, generalized equations (variational inequali...

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Bibliographic Details
Published in:SIAM journal on control and optimization Vol. 38; no. 3; pp. 947 - 970
Main Author: Jourani, Abderrahim
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 2000
Subjects:
Banach spaces
Convex analysis
Inequality
Linear programming
Mathematical functions
Mathematical programming
Sensitivity analysis
ISSN:0363-0129, 1095-7138
Online Access:Get full text
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Summary:Our aim is to present sufficient conditions ensuring Hoffman'serror bound for lower semicontinuous nonconvex inequality systems and to analyze its impact on the local controllability, implicit function theorem for (non-Lipschitz) multivalued mappings, generalized equations (variational inequalities), and sensitivity analysis and on other problems like Lipschitzian properties of polyhedral multivalued mappings as well as weak sharp minima or linear conditioning. We show how the information about our sufficient conditions can be used to provide a computable constant such that Hoffman's error bound holds. We also show that this error bound is nothing but the classical Farkas lemma for linear inequality systems. In the latter case our constant may be computed explicitly.
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ISSN:0363-0129
1095-7138
DOI:10.1137/S0363012998339216