Neural network for nonsmooth pseudoconvex optimization with general constraints

In this paper, a one-layer recurrent projection neural network is proposed for solving pseudoconvex optimization problems with general convex constraints. The proposed network in this paper deals with the constraints into two parts, which brings the network simpler structure and better properties. By the Tikhonov-like regularization method, the proposed network need not estimate the exact penalty parameter in advance. Moreover, comparing with some existing neural networks, the proposed network can solve more general constrained pseudoconvex optimization problems. When the solution of the proposed network is bounded, it converges to the optimal solution set of considered optimization problem, which may be nonsmooth and nonconvex. Meantime, some sufficient conditions are presented to guarantee the boundedness of the solution of the proposed network. Numerical examples with simulation results are given to illustrate the effectiveness and good characteristics of the proposed network for solving constrained pseudoconvex optimization.