Please use this identifier to cite or link to this item: 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
Keywords: Nonsmooth nonconvex optimization
Smoothing methods
Convergence
Regularized optimization
Penalty function
Non-Lipschitz
Trust region Newton method
Issue Date: 2013
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM Journal on optimization, 2013, v. 23, no. 3, p. 1528–1552 How to cite?
Journal: SIAM Journal on optimization 
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.
URI: http://hdl.handle.net/10397/7014
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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