Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/6108
Title: Smoothing projected gradient method and its application to stochastic linear complementarity problems
Authors: Zhang, C
Chen, X 
Keywords: Smoothing projected gradient method
Nonsmooth
Nonconvex
onstrained optimization
Stochastic linear complementarity problem
Image restoration
Issue Date: 2009
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on optimization, 2009, v. 20, no. 2, p. 627-649 How to cite?
Journal: SIAM journal on optimization 
Abstract: A smoothing projected gradient (SPG) method is proposed for the minimization problem on a closed convex set, where the objective function is locally Lipschitz continuous but nonconvex, nondifferentiable. We show that any accumulation point generated by the SPG method is a stationary point associated with the smoothing function used in the method, which is a Clarke stationary point in many applications. We apply the SPG method to the stochastic linear complementarity problem (SLCP) and image restoration problems. We study the stationary point defined by the directional derivative and provide necessary and sufficient conditions for a local minimizer of the expected residual minimization (ERM) formulation of SLCP. Preliminary numerical experiments using the SPG method for solving randomly generated SLCP and image restoration problems of large sizes show that the SPG method is promising.
URI: http://hdl.handle.net/10397/6108
ISSN: 1052-6234
EISSN: 1095-7189
DOI: 10.1137/070702187
Rights: © 2009 Society for Industrial and Applied Mathematics
Appears in Collections:Journal/Magazine Article

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