A novel neural network to nonlinear complex-variable constrained nonconvex optimization

Abstract

In this paper, a novel complex-valued neural network (CVNN) is proposed to investigate a nonlinear complex-variable nonconvex optimization problem (CVNOP) subject to general types of convex constraints, including inequality and bounded as well as equality constraints. The designed neural network is available to search the critical point set of CVNOP. In contrast with other related neural networks to complex-variable optimization problem, network herein contains fewer neurons and does not depend on exact penalty parameters. To our best knowledge, this is the first attempt to exploit the neural network to solve nonconvex complex-variable optimization problem. Furthermore, the presented network is also capable of solving convex or nonconvex real-variable optimization problem (RVNOP). Different from other existing neural networks for RVNOP, our network avoids the redundant computation of inverse matrix and relaxes some additional assumptions, comprising the objective function is bounded below over the feasible region or the objective function is coercive. Several numerical illustrations and practical results in beamforming provide the viability of the proposed network.