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Global convergence of the Polak-Ribière-Polyak conjugate gradient method with an Armijo-type inexact line search for nonconvex unconstrained optimization problems. (English) Zbl 1198.65091
Summary: We propose two algorithms for nonconvex unconstrained optimization problems that employ Polak-Ribière-Polyak conjugate gradient formula and new inexact line search techniques. We show that the new algorithms converge globally if the function to be minimized has Lipschitz continuous gradients. Preliminary numerical results show that the proposed methods for particularly chosen line search conditions are very promising.
MSC:
65H10Systems of nonlinear equations (numerical methods)
90C26Nonconvex programming, global optimization