A three-term conjugate gradient method with sufficient descent property for unconstrained optimization

Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed general method. … Read more

Extended Barzilai-Borwein method for unconstrained minimization problems

In 1988, Barzilai and Borwein presented a new choice of step size for the gradient method for solving unconstrained minimization problems. Their method aimed to accelerate the convergence of the steepest descent method. The Barzilai-Borwein method requires few storage locations and inexpensive computations. Therefore, several authors have paid attention to the Barzilai-Borwein method and have … Read more