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.

本文提出了一种新颖的复值神经网络（CVNN），以研究受凸约束（包括不等式和有界以及等式约束）的一般类型约束的非线性复杂变量非凸优化问题（CVNOP）。设计的神经网络可用于搜索CVNOP的临界点集。与其他涉及复杂变量优化问题的相关神经网络相反，本文的网络包含较少的神经元，并且不依赖于精确的罚分参数。据我们所知，这是利用神经网络解决非凸复变量优化问题的首次尝试。此外，所提出的网络还能够解决凸或非凸实变量优化问题（RVNOP）。与其他现有的RVNOP神经网络不同，我们的网络避免了逆矩阵的冗余计算，并放宽了一些额外的假设，其中包括目标函数在可行区域以下或目标函数是强制性的。波束成形中的一些数字图示和实际结果提供了所提出网络的可行性。