## Globally convergent Polak-Ribière-Polyak conjugate gradient methods under a modified Wolfe line search.(English)Zbl 1185.65100

It is well known that global convergence has not been established for the Polak-Ribiere-Polyak (PRP) conjugate gradient method using the standard Wolfe conditions. In this paper some global convergence results for the PRP-type conjugate gradient method are established, where the step-length is computed by a modified Wolfe line search. Some efficient choices for $$\beta_k$$ which can ensure the descent property of the search direction are also discussed. Preliminary numerical experiments on a set of a large-scale problems show that the computational efficiency of the PRP method is not deteriorated.

### MSC:

 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming 90C06 Large-scale problems in mathematical programming 65Y20 Complexity and performance of numerical algorithms

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