Collaborative neurodynamic optimization for solving nonlinear equations

Abstract

A distributed optimization method for solving nonlinear equations with constraints is developed in this paper. The multiple constrained nonlinear equations are converted into an optimization problem and we solve it in a distributed manner. Due to the possible presence of nonconvexity, the converted optimization problem might be a nonconvex optimization problem. To this end, we propose a multi-agent system based on an augmented Lagrangian function and prove that it converges to a locally optimal solution to an optimization problem in the presence of nonconvexity. In addition, a collaborative neurodynamic optimization method is adopted to obtain a globally optimal solution. Three numerical examples are elaborated to illustrate the effectiveness of the main results.