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Convergence of the Polak-Ribiére-Polyak conjugate gradient method. (English) Zbl 1120.49027

In this paper, an new kind of Armijo-type line search has been proposed for guaranteeing the global convergence of the Polak-Ribiére-Polyak conjugate gradient method for unconstrained minimizing functions that have Lipschitz continouous partial derivatives. The global convergence and linear convergence rate were analyzed under some mild conditions. Numerical results show that the proposed method with the new Armijo-type line search is more efficient than other similar methods in practical computation.

MSC:

49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming

Software:

minpack
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References:

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