New three-term conjugate gradient method with guaranteed global convergence

Abstract

The conjugate gradient method is one of the most effective methods to solve the unconstrained optimization problems. In this paper, we develop a new three-term conjugate gradient (TTCG) method by applying the Powell symmetrical technique to the Hestenes–Stiefel method. The proposed method satisfies both the sufficient descent property and the conjugacy condition , which do not rely on any line search. Under the standard Wolfe line search, the global convergence of the proposed method is also established. The numerical results also show that the proposed method is very effective and interesting by comparing with other TTCG methods using a classical set of test problems.