A projection type steepest descent neural network for solving a class of nonsmooth optimization problems

In this paper, a new one layer recurrent neural network is proposed to solve nonsmooth optimization problems with nonlinear inequality and linear equality constraints. Model is based on a differential inclusion and combines steepest descent and gradient projection methods simultaneously. Any solution trajectory of the introduced differential inclusion converges globally to the optimal solution set of the corresponding optimization problem. Comparing with the existing models for solving nonsmooth optimization problems, there does not exist any penalty parameter in the structure of the new model and the model has simple structure. Moreover, the optimal solution of the original optimization problem is equivalent to the equilibrium point of the proposed neural network. Some illustrative examples are presented to show the effectiveness and performance of the proposed neural network.