Research On Two Types Of Complex-variable Optimization Problems Based On Recurrent Neural Networks

As one of the significant study theme of science and hard technology,optimization problem has been expanded from real number domain to complex number domain with the continuous progress of science and engineering technology.How to solve complex-variable optimization problem quickly and efficiently has become a difficult problem.Artificial neural network has the characteristics of large-scale parallel computation and fast convergence,so using the idea of neural network to solve complex-variable optimization problems has become a hot research topic at home and abroadDifferent from the traditional method to solve the complex-variable optimization problem,it is necessary to separate the real part from the imaginary part to transform the problem into a real value optimization problem.At the same time,because the real valued functions in the complex range are non-analytic,the previous real valued neural networks can not directly solve the complex-variable optimization problems.In order to avoid the above problems,based on CR-calculus,two different models are proposed to solve complex-variable convex optimization and complex-variable pseudo-convex optimization respectively.First,for a class of complex-variable convex optimization problems with equality and inequality constraints,a novel single-layer recurrent neural network model without precise penalty factor is presented based on the thought ofCR-calculus and penalty function.Compared with the existing neural networks,this neural network does not need to figure the precise penalty factor,has no additional demands for the choice of initial points,has a simpler structure hierarchy,and can also solve the real-variable convex optimization problem.It is proved by theoretical analysis that the trajectory of the model will enter the feasible region in finite time and converge to the optimal solution of complex-variable convex optimization problem.Finally,the correctness of the theory and the effectiveness of the neural network are verified by the simulation experiment.Second,for a class of complex-variable pseudo-convex optimization problems subject to linear equality and inequality constraints,based on the idea ofCR-calculus and penalty function,a novel single-layer recurrent neural network model is proposed.Compared with the existing neural networks,the structure and hierarchy of the neural network model are simple,the application range is wide,and there is no need to calculate the exact penalty parameters,and there is no additional demands for the choice of initial points.Moreover,it is proved that the complex-variable recurrent neural network has a global solution,which enters the feasible domain of the original complex optimization problem in a finite time and stays in it forever,and will converge to the optimal solution of the original complex-variable optimization problem.Finally,different experiments are used to prove the effectiveness of the complex-variable recurrent neural network proposed.