Neural network for constrained nonsmooth optimization using Tikhonov regularization. (March 2015)

• Record Type: Journal Article
• Authors: Qin, Sitian; Fan, Dejun; Wu, Guangxi; Zhao, Lijun
• Is Part Of: Neural networks. Volume 63(2015:Mar.)
• Page Start: 272
• Page End: 281
• Publication Date: 2015-03
• Subjects: One-layer neural network -- Nonsmooth convex optimization problems -- Tikhonov regularization method; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2014.12.007
• Languages: English
• ISSNs: 0893-6080

Abstract

Abstract: This paper presents a one-layer neural network to solve nonsmooth convex optimization problems based on the Tikhonov regularization method. Firstly, it is shown that the optimal solution of the original problem can be approximated by the optimal solution of a strongly convex optimization problems. Then, it is proved that for any initial point, the state of the proposed neural network enters the equality feasible region in finite time, and is globally convergent to the unique optimal solution of the related strongly convex optimization problems. Compared with the existing neural networks, the proposed neural network has lower model complexity and does not need penalty parameters. In the end, some numerical examples and application are given to illustrate the effectiveness and improvement of the proposed neural network.