Paper Info
Title
Perturbation Analysis of Error Bounds for Quasi-subsmooth Inequalities and Semi-infinite Constraint Systems
Abstract
The stability of error bounds is significant in optimization theory and applications. Based on either the linearity assumption or the convexity and finite dimension assumption, several authors have focused on perturbation analysis of error bounds and obtained valuable results. Mainly motivated by Ngai, Kruger, and Théra [SIAM J. Optim., 20 (2010), pp. 2080-2096], in a general Banach space, we study the stability of error bounds for inequalities determined by proper lower semicontinuous quasi-subsmooth functions which are a very large class of nonconvex functions (in particular, approximate convex functions, primal-lower-nice functions, and convexly composite functions satisfying the Robinson qualification). We also consider the stability of error bounds for infinite constraint systems determined by infinitely many uniformly quasi-subsmooth functions. In particular, we extend the main results of Ngai, Kruger, and Théra to the infinite dimensional and nonconvex setting.
Year
DOI
Venue
2012
10.1137/100806199
SIAM Journal on Optimization
Keywords
Field
DocType
nonconvex function,error bounds,perturbation analysis,infinite dimensional,siam j. optim,quasi-subsmooth inequalities,quasi-subsmooth function,robinson qualification,error bound,nonconvex setting,infinite constraint system,semi-infinite constraint systems,finite dimension assumption,linearity assumption,subdifferential
Mathematical optimization,Convexity,Perturbation theory,Semi-infinite,Linearity,Banach space,Subderivative,Convex function,Mathematics
Journal
Volume
Issue
ISSN
22
1
1052-6234
Citations 
PageRank 
References 
2
0.63
20
Authors
2
Name
Order
Citations
PageRank
Xi Yin Zheng123624.17
Zhou Wei220.96