A Self-Adjusting Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition

In this paper, a self-adjust conjugate gradient method is proposed for solving unconstrained problems, which can generate sufficient descent directions at each iteration. Different from the existent methods, a dynamical adjustment of conjugacy condition in our proposed method is developed, which can be regarded as the inheritance and development of properties of standard Hestenes–Stiefel method. Under mild condition, we show the proposed method convergent globally even if the objective function is nonconvex. Numerical results illustrate that our method can efficiently solve the test problems and therefore is promising.