Result: On Best Approximation by Nonconvex Sets and Perturbation of Nonconvex Inequality Systems in Hilbert Spaces: On best approximation by nonconvex sets and perturbation of nonconvex inequality systems in Hilbert spaces

Title:
On Best Approximation by Nonconvex Sets and Perturbation of Nonconvex Inequality Systems in Hilbert Spaces: On best approximation by nonconvex sets and perturbation of nonconvex inequality systems in Hilbert spaces
Authors:
K. F. Ng, Chong Li
Source:
SIAM Journal on Optimization. 13:726-744
Publisher Information:
Society for Industrial & Applied Mathematics (SIAM), 2002.
Publication Year:
2002
Subject Terms:
Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Approximation with constraints, strong CHIP, 0211 other engineering and technologies, nonlinear inequality system, 02 engineering and technology, 0101 mathematics, best approximation, the basic constraint qualification condition, 01 natural sciences, nonlinear constraint, generalized Mangasarian-Fromowitz constraint qualification and regularity
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1095-7189
1052-6234
DOI:
10.1137/s1052623402401373
Access URL:
https://zbmath.org/1848720
https://doi.org/10.1137/s1052623402401373
http://www.math.zju.edu.cn/webpagenew/UploadFiles/AttachFiles/20069317569350.pdf
https://epubs.siam.org/doi/10.1137/S1052623402401373
https://dblp.uni-trier.de/db/journals/siamjo/siamjo13.html#LiN02
Accession Number:
edsair.doi.dedup.....614faec77d521f02a124c50b73b5d92c
Database:
OpenAIRE

Further Information

Summary: By virtue of convexification techniques, we study best approximations to a closed set \(C\) in a Hilbert space as well as perturbation conditions relative to \(C\) and a nonlinear inequality system. Some results on equivalence of the best approximation and the basic constraint qualification are established.