Smoothing Neural Network For Solving Optimization With Application In Image Processing

As we all know,with nonsmooth objective function of optimization problem existed widely in a large number of scientific research, engineering, economic and other fields.Most researchers use approximation method of target function, to a certain extent, it can solve some optimization problems.However, the calculation of higher dimensions and more complex optimization problems, the calculation time is that we have to consider, the emergence of the neural network and its adaptability and parallelism makes computing speed increased. In recent years, the neural network method applied to solve the nonsmooth optimization problem, aiming at this phenomenon, this paper mainly discusses the type of the constraint conditions with nonsmooth optimization problem solving.In this paper, a smoothing neural network(SNN) is proposed for a class of constrained non-Lipschitz optimization problems, where the objective function is the sum of a nonsmooth and a non-Lipschitz function. Using the smoothing approximate technique, the proposed neural network is modeled by a differential equation,which can be implemented easily.Under the level bounded condition on the objective function, we prove the global existence and uniform boundedness of the solutions of the SNN any initial point.The uniqueness of the solution of the SNN is provided under the Lipschitz property of smoothing function. Then we show that any accumulation point of the solution of the SNN is a stationary point of the optimization problems.Image restoration is presented to illustrate the theoretical results and show the efficiency of the SNN. By adjusting parameters show the advantages of the SNN.