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http://hdl.handle.net/10397/7014
Title: | Optimality conditions and a smoothing trust region newton method for nonlipschitz optimization | Authors: | Chen, X Niu, L Yuan, Y |
Issue Date: | 2013 | Source: | SIAM Journal on optimization, 2013, v. 23, no. 3, p. 1528–1552 | Abstract: | Regularized minimization problems with nonconvex, nonsmooth, perhaps non-Lipschitz penalty functions have attracted considerable attention in recent years, owing to their wide applications in image restoration, signal reconstruction, and variable selection. In this paper, we derive affine-scaled second order necessary and sufficient conditions for local minimizers of such minimization problems. Moreover, we propose a global convergent smoothing trust region Newton method which can find a point satisfying the affine-scaled second order necessary optimality condition from any starting point. Numerical examples are given to demonstrate the effectiveness of the smoothing trust region Newton method. | Keywords: | Nonsmooth nonconvex optimization Smoothing methods Convergence Regularized optimization Penalty function Non-Lipschitz Trust region Newton method |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM Journal on optimization | ISSN: | 1052-6234 | EISSN: | 1095-7189 | DOI: | 10.1137/120871390 | Rights: | © 2013 Society for Industrial and Applied Mathematics |
Appears in Collections: | Journal/Magazine Article |
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