A gradient-type noise-tolerant finite-time neural network for convex optimization

Abstract

As one of powerful methods for solving optimization problems, the gradient-type neural network has attracted the attention of many scholars. Up to now, there are few studies on finite-time convergence and the ability of noise tolerance of gradient-type networks. Motivated by the superior performance of various activation functions and advantages of gradient-type networks for solving constrained optimization, this paper aims to introduce a suitable activation function in a gradient-type neural network to solve convex optimization. It is shown that the state solution of the network converges to an optimal solution of the original convex optimization and the convergence time is finite under mild conditions. The capability of the network to suppress bounded noises is also analyzed theoretically. Superior to existing models for constrained optimization, the resulting network model not only has fast convergence but also can tolerate additive noises. Some numerical results are reported, including the results for smooth and nonsmooth problems, to show that the presented network is effective for convex constrained problems in the absence and presence of additive noises.