A Novel Neural Network for Solving Nonsmooth Nonconvex Optimization Problems

In this paper, a novel recurrent neural network (RNN) is presented to deal with a kind of nonsmooth nonconvex optimization problem in which the objective function may be nonsmooth and nonconvex, and the constraints include linear equations and convex inequations. Under certain suitable assumptions, from an arbitrary initial state, each solution to the proposed RNN exists globally and is bounded, and it enters the feasible region within a limited time. Moreover, the solution to the RNN with an arbitrary initial state can converge to the critical point set of the optimization problem. In particular, the RNN does not need the following: 1) abounded feasible region; 2) the computation of an exact penalty parameter; or 3) the initial state being chosen from a given bounded set. Numerical experiments are provided to show the effectiveness and advantages of the RNN.