一种解决受约束的复变凸优化问题的新型神经网络

Novel Neural Network for Solving Constrained Complex-variable Convex Optimization Problems

复变优化问题广泛应用于信号识别与机器人控制诸多领域,是当下国内外研究的热点.本文针对一类带等式与不等式约束的复变凸优化问题,提出一种可解决此类问题的单层循环神经网络模型.首先,通过理论分析证明在有限时间内该模型的轨迹将进入可行域,并收敛于复变凸优化问题的最优解.其次,通过仿真模拟实验,验证了文中理论的正确性,以及该神经网络的有效性.最后,与目前已经提出的神经网络相比,该神经网络不需要计算精确惩罚参数,对初始点选取没有特殊要求,结构较为简单,为单层结构.

The complex-variable optimization problem is widely used in signal recognition and robot control,which is a hot research topic at home and abroad.In this paper,to solve complex-variable convex optimization problems with equality and inequality constraints,a one-ayer recurrent neural network is proposed.Firstly Jby using theoretical analysis method,it is proved that the trajectory of the model can enter the feasible region in a limited time and eventually converge to the optimal solution of the complex-variable convex optimization problem.Secondly,the validity of the theory and the validity of the neural network are verified by simulation experiments.Finally,compared with proposed neural network existed,this neural network has a simpler structure which is one-ayer structure without special requirements for the selection of initial points,and it does not need to calculate accurate penalty parameters.