An improved preconditioned conjugate gradient method for unconstrained optimization problem with application in Robot arm control

Abstract

Abstract This work suggests improved conjugate gradient methods for enhancing the efficiency and robustness of the classical conjugate gradient methods. The study modifies the diagonal of the inverse Hessian approximation of the Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi‐Newton update in order to build a preconditioner for nonlinear conjugate gradient (NCG) methods applied to large‐scale unconstrained optimization problems. Damping techniques were embedded into the algorithm to impose the positive definiteness of the diagonal approximation. This made the methods easy to use and presented a viable way to increase the effectiveness of unconstrained optimization techniques. Experimental findings from a collection of benchmark problems demonstrate the efficiency and robustness of the proposed method when compared to five other existing NCG algorithms. Moreover, the successful application of the algorithm to manipulate robotic planar motion control systems with 3 degrees of freedom has been demonstrated, highlighting the practicality of the proposed approach.

Keywords

• damped techniques
• diagonal quasi‐Newton
• preconditioned conjugate gradient
• robotic control
• unconstrained optimization