A Sufficiently Descending Three-Term Nonlinear Conjugate Gradient Method for Unconstrained Optimization Problems with Application

This paper presents a new nonlinear conjugate gradient method in which the new search direction comprises three terms, and the step length is required to satisfy the well-known strong Wolfe line search strategy. The new three-term search direction is a modification of a recently published one in the literature. Unlike the search direction that was modified, the new search direction satisfies the important sufficient descent condition without imposing additional conditions or restrictions. We discuss the convergence results of the proposed method under the assumption that the function is smooth and its gradient is Lipschitz continuous. We present numerical experiments on a collection of benchmark test problems and compare the new method’s performance with some existing ones. Finally, we apply the method to robotic arm motion control.