article · CUHK Digital Repository (Chinese University of Hong Kong) · 2007
Some nonconvex geometric results in variational analysis and optimization.
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Abstract
In this thesis, we consider the following two important subjects in the modern variational analysis for the corresponding nonconvex/nonmonotone and nonsmooth cases: geometric results and the variational inequality problem. By using the variational technique, we first present several nonsmooth (nonconvex) geometric results (including an approximate projection result, an extended extremal principle, nonconvex separation theorems, a nonconvex generalization of the Bishop-Phelps theorem and a separable point result) which extend some fundamental theorems in linear functional analysis, convex analysis and optimization theory. Then, by transforming the variational inequality problem into equivalent optimization problems, we establish some error bound result for the nonsmooth and nonmonotone variational inequality problem.
Cite this paper
(2007). Some nonconvex geometric results in variational analysis and optimization. CUHK Digital Repository (Chinese University of Hong Kong).
“Some nonconvex geometric results in variational analysis and optimization.” CUHK Digital Repository (Chinese University of Hong Kong), 2007.
2007. “Some nonconvex geometric results in variational analysis and optimization.” CUHK Digital Repository (Chinese University of Hong Kong).
(2007) ‘Some nonconvex geometric results in variational analysis and optimization’, CUHK Digital Repository (Chinese University of Hong Kong).
@article{anon2007some,
title = {{Some nonconvex geometric results in variational analysis and optimization.}},
journal = {CUHK Digital Repository (Chinese University of Hong Kong)},
year = {2007}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.