A scaled Polak-Ribi $\stackrel{`}{e}$re-Polyak conjugate gradient algorithm for constrained nonlinear systems and motion control

This paper proposes Polak-Ribi $\stackrel{`}{e}$re-Polyak (PRP) conjugate gradient (CG) directions based on two efficient scaling strategies. The first scaling parameter is determined by approaching the quasi-Newton direction, and the second by utilizing the well-known Barzilai-Borwein approach. In addition, we proposed two directions that satisfy the sufficient descent criterion regardless of the line search strategy. The proposed directions lead to a matrix-free algorithm for solving monotone-constrained nonlinear systems. The proposed algorithm's global convergence analysis is presented using some underlying assumptions. Furthermore, a detailed numerical comparison with other existing algorithms revealed that the proposed algorithm is both efficient and effective. Finally, the proposed technique is applied to the motion control problem of a two-joint planar robotic manipulator.