A Discrete Neural Network For Solving Degenerate Quadratic Programming Problems

The quadratic optimization problem plays an important role in scientific research and engineering applications,such as restoration analysis,signal and image processing,manufacturing,optimal control,and system identification.However,the traditional optimization algorithm can hardly implement on hardware,and real-time performance is poor.The emergence of the neural network optimization algorithm overcomes two problems of the traditional optimization algorithm in hardware implementation and real-time processing,that is because: on the one hand,the neural network is easy to implement on circuit,the dynamic solving process of neural network optimization algorithm is parallel and distributed,therefore,the running time of the neural network method is much less than that of the traditional optimization algorithm.Degenerate quadratic optimization is very common in engineering practice and life practice,in order to solve this problem,this paper proposes a discrete time neural network optimization algorithm.We use Lyapunov function to prove its stability,and the effectiveness of the algorithm is verified by experimental simulation.Furthermore,the algorithm is applied to portfolio selection problem,and the optimal portfolio is obtained under certain conditions.The main research contents and innovations point of this paper are as follows:1.We propose a discrete time neural network optimization algorithm for solving the degenerate quadratic optimization problems.For the general degenerate quadratic optimization algorithm,firstly,we construct the corresponding Lagrange function and combine the saddle point theorem,use the projection method to find the corresponding projection equation.According to the projection equation,we can propose the corresponding discrete time neural network model.We construct the Lyapunov function,which verifies that the network is global convergence under given conditions.The simulation results show the effectiveness of the algorithm in solving the quadratic degenerate optimization problems.2.A class of optimal portfolio problem is studied by using the proposed neural network optimization algorithm.Now,stock market is unprecedented hot,many investors' ability of anti-risk is poor,so improve the investors' ability of anti-risk,while increasing the rate of return is very important.By analyzing the Markowitz mean-variance model,we transform the optimal portfolio problem into quadratic optimization problem and solve it by neural network algorithm.Finally,we find the portfolio with the smallest risk factor in the given income case.