A New Class of Hybrid Spectral Conjugate Gradient Approach for Unconstrained Optimization and Motion Control Problems

This article presents an efficient hybrid Conjugate gradient (CG) method for solving largescale unconstrained optimization problems. The search direction of the proposed method of four distinct classical CG parameters, which consist of descent (DY), Fletcher-Reeves (FR), Hestenes-Stiefel (HS), and Polak-Ribi\'{e}re-Polyak (PRP) parameters. The welcoming advantage of the new method is that the direction can be descent in any case of the CG parameter and the line search type being used. We prove the global convergence by employing a modified version of Wolfe line search conditions. Numerical experiments on some benchmark test problems were provided to ascertain the efficiency of the method. Lastly, the method was applied to solve problems arising from the motion control of the robot manipulator.