A One-Layer Projection Neural Network for Nonsmooth Optimization Subject to Linear Equalities and Bound Constraints

• Published in: IEEE transaction on neural networks and learning systems Vol. 24; no. 5; pp. 812 - 824
• Main Authors: Liu, Qingshan, Wang, Jun
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-05-2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Artificial intelligence; Biological neural networks; Computer science; control theory; systems; Computer Simulation; Connectionism. Neural networks; Convergence; Differential inclusion; Exact sciences and technology; global convergence; Humans; Linear programming; Lyapunov function; Mathematical model; Neural networks; Neural Networks (Computer); Nonlinear Dynamics; nonsmooth optimization; Operations research; Optimization; Problem Solving; projection neural network; Recurrent neural networks; Studies; Convex set; Generalized function; Network management; Modeling; Linear operator; nonsmooth optimization; Optimization; Projection method; projection neural network; Nonsmooth analysis; Efficiency; Convex function; Mathematical programming; Recurrent neural nets; global convergence; Linear programming; Neural network; Distributed system; Set constraint; Projection operator; Optimal solution; Equality constraint; Objective function; Differential inclusion; Lyapunov function
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2013.2244908

This paper presents a one-layer projection neural network for solving nonsmooth optimization problems with generalized convex objective functions and subject to linear equalities and bound constraints. The proposed neural network is designed based on two projection operators: linear equality constraints, and bound constraints. The objective function in the optimization problem can be any nonsmooth function which is not restricted to be convex but is required to be convex (pseudoconvex) on a set defined by the constraints. Compared with existing recurrent neural networks for nonsmooth optimization, the proposed model does not have any design parameter, which is more convenient for design and implementation. It is proved that the output variables of the proposed neural network are globally convergent to the optimal solutions provided that the objective function is at least pseudoconvex. Simulation results of numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.