A Sufficient Descent Property for a Different Parameter to Enhance Three-Term Method

In this paper, we derive a new parameter k-1 for the three-term CG (N3T) algorithm for solving unconstrained optimization problems. As demonstrated by its calculations and proof, the parameter k-1 worth is determined by T , and the study mentions four different types of T . The search directions of this algorithm are always sufficiently descent when using strong Wolfe line search (SWC). Under reasonable assumptions, the proposed algorithm achieves global convergence. The numerical comparison demonstrates that our proposed method works well for solving unconstrained optimization problems.