A new scaled BFGS method for convex constraints monotone systems: Applications in motion control

This paper introduces a new version of the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm, characterized as a scaled memoryless, projection-based, and derivative-free method for finding approximate solutions of monotone nonlinear equations with convex constraints. The optimal value of the scaling parameter is achieved by minimizing the BFGS update matrix. The theoretical analysis is performed to demonstrate the global convergence of the approach. Numerical analysis and comparisons with prior results indicate that the proposed approach has superior performance for CPU time, iteration count, and function evaluations. The new algorithm is used to solve the motion control issue of a two-jointed coplanar robot manipulator.