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Global convergence of modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property. (English) Zbl 1168.65030
The authors study two modifications of the conjugate gradient method for solving an unconstrained optimization problem. The first and second sections of this article present an outline of the conjugate gradient method and an overview of the existing literature, with a particular focus on the Polak-Ribière-Polyak implementation. In the third section the authors provide the details of the two proposed algorithms, followed by a study of their convergence properties (section 4) where several theorems are stated and proved.
The last two sections of the paper contain the results of extensive numerical experimentation and suggestions for future work.

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C26 Nonconvex programming, global optimization
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