An Adaptive Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition

Abstract

In this paper, an adaptive three-term conjugate gradient method is proposed for solving unconstrained problems, which generates sufficient descent directions at each iteration. Different from the existent methods, a dynamical adjustment between Hestenes–Stiefel and Dai–Liao conjugacy conditions in our proposed method is developed. Under mild condition, we show that the proposed method converges globally. Numerical experimentation with the new method indicates that it efficiently solves the test problems and therefore is promising.