Smoothing neural network for constrained convex optimization with global attractivity

A smoothing neural network (SNN) can be proposed for solving a kind of constrained convex problems, which has wide applications in image restoration. The optimization model is a nonsmooth convex problem with convex constraint defined by a class of affine equalities. Thanks to the smoothing methods, the SNN can be modeled by a differential equation instead of a differential inclusion and it can be implemented easily. When the objective function is the level bounded in the feasible region, the solution to the SNN with initial point in the feasible set is global existent and unique, where the uniqueness of the solution to the SNN is based on the special structure of the proposed smoothing functions. Moreover, any accumulation point of the solution to the SNN is an optimal solution of the considered optimization problem. Furthermore, the illustrative example shows the correctness of the results in this paper, and the good performance of the SNN.