An Adaptive Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition
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.
KeywordsThree-term conjugate gradient method Sufficient descent condition Conjugacy condition Global convergence
Mathematics Subject Classification49M37 65K05 90C53
We are grateful to the anonymous referees and editor for their useful comments, which have made the paper clearer and more comprehensive than the earlier version. We thank Professors W. W. Hager and H. Zhang for their CG_DESCENT code for numerical comparison.