Solution of a System of Nonlinear Convex Constrained Monotone Equations using BFGS Method of Projection Approach with Application in Motion Control

Abstract

This paper presents the scaling memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) method for solving a system of nonlinear convex constrained monotone equations. The optimal value of the scaling parameter is obtained by minimizing the condition number. A derivative-free memoryless BFGS projection-based algorithm is proposed. The global convergence of the algorithm is obtained analytically and some test problems are solved numerically. The computed results are compared with the available results in the literature. It is observed that the proposed algorithm performs well in terms of CPU time, number of iterations and function evaluations. Furthermore, the proposed method is successfully applied to robot manipulator motion control.