An efficient one-layer recurrent neural network for solving a class of nonsmooth optimization problems

Constrained optimization problems have a wide range of applications in science, economics, and engineering. In this paper, a neural network model is proposed to solve a class of nonsmooth constrained optimization problems with a nonsmooth convex objective function subject to nonlinear inequality and affine equality constraints. It is a one-layer non-penalty recurrent neural network based on the differential inclusion. Unlike most of the existing neural network models, there is neither a penalty parameter nor a penalty function in its structure. It has less complexity which leads to the easier implementation of the model for solving optimization problems. The equivalence of optimal solutions set of the main optimization problem and the equilibrium points set of the model is proven. Moreover, the global convergence and the stability of the introduced neural network are shown. Some examples including the L1-norm minimization problem are given and solved by the proposed model to illustrate its performance and effectiveness.