Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/20959
Title: Smoothing neural network for constrained non-lipschitz optimization with applications
Authors: Bian, W
Chen, X 
Keywords: Image and signal restoration
Non-Lipschitz optimization
Smoothing neural network
Stationary point
Variable selection
Issue Date: 2012
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on neural networks and learning systems, 2012, v. 23, no. 3, 6123210, p. 399-411 How to cite?
Journal: IEEE transactions on neural networks and learning systems 
Abstract: In this paper, a smoothing neural network (SNN) is proposed for a class of constrained non-Lipschitz optimization problems, where the objective function is the sum of a nonsmooth, nonconvex function, and a non-Lipschitz function, and the feasible set is a closed convex subset of. Using the smoothing approximate techniques, the proposed neural network is modeled by a differential equation, which can be implemented easily. Under the level bounded condition on the objective function in the feasible set, we prove the global existence and uniform boundedness of the solutions of the SNN with any initial point in the feasible set. The uniqueness of the solution of the SNN is provided under the Lipschitz property of smoothing functions. We show that any accumulation point of the solutions of the SNN is a stationary point of the optimization problem. Numerical results including image restoration, blind source separation, variable selection, and minimizing condition number are presented to illustrate the theoretical results and show the efficiency of the SNN. Comparisons with some existing algorithms show the advantages of the SNN.
URI: http://hdl.handle.net/10397/20959
ISSN: 2162-237X
EISSN: 2162-2388
DOI: 10.1109/TNNLS.2011.2181867
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