A differential inclusion-based approach for solving nonsmooth convex optimization problems

Abstract

This article presents a differential inclusion-based neural network for solving nonsmooth convex programming problems with inequality constraints. The proposed neural network, which is modelled with a differential inclusion, is a generalization of the steepest descent neural network. It is proved that the set of the equilibrium points of the proposed differential inclusion is equal to that of the optimal solutions of the considered optimization problem. Moreover, it is shown that the trajectory of the solution converges to an element of the optimal solution set and the convergence point is a globally asymptotically stable point of the proposed differential inclusion. After establishing the theoretical results, an algorithm is also designed for solving such problems. Typical examples are given which confirm the effectiveness of the theoretical results and the performance of the proposed neural network.