A one-layer recurrent neural network for nonsmooth pseudoconvex optimization with quasiconvex inequality and affine equality constraints

Abstract

As two important types of generalized convex functions, pseudoconvex and quasiconvex functions appear in many practical optimization problems. The lack of convexity poses some difficulties in solving pseudoconvex optimization with quasiconvex constraint functions. In this paper, we propose a one-layer recurrent neural network for solving such problems. We prove that the state of the proposed neural network is convergent from the feasible region to an optimal solution of the given optimization problem. We show that the proposed neural network has several advantages over the existing neural networks for pseudoconvex optimization. Specifically, the proposed neural network is applicable to optimization problems with quasiconvex inequality constraints as well as affine equality constraints. In addition, parameter matrix inversion is avoided and some assumptions on the objective function and inequality constraints in existing results are relaxed. We demonstrate the superior performance and characteristics of the proposed neural network with simulation results in three numerical examples.