title: Neural network for constrained nonsmooth optimization using Tikhonov regularization.
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.
authors.affiliation: Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, PR China. Electronic address: qinsitian@163.com.
authors.forename: Sitian
authors.initials: S
authors.lastname: Qin
authors.affiliation: Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, PR China. Electronic address: fandejun2066@126.com.
authors.forename: Dejun
authors.initials: D
authors.lastname: Fan
authors.affiliation: Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, PR China.
authors.forename: Guangxi
authors.initials: G
authors.lastname: Wu
authors.affiliation: School of Automobile Engineering, Harbin Institute of Technology at Weihai, Weihai 264209, PR China.
authors.forename: Lijun
authors.initials: L
authors.lastname: Zhao
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D016571:Neural Networks, Computer
keywords: Nonsmooth convex optimization problems; One-layer neural network; Tikhonov regularization method