Abstract
In this paper, by taking a little modification to the Hestenes–Stiefel method, we propose a new way to construct descent directions satisfying the sufficient descent condition. Also, an adaptive conjugacy condition and a intrinsic self-restarting mechanism are revealed, a dynamical adjustment can be regarded as the inheritance and development of properties of standard Hestenes–Stiefel method. Furthermore, we establish global convergence for general nonconvex objective function under mild condition. Numerical results show that our presented methods can be efficient for solving large-scale test problems and therefore is promising.
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