## $$n$$-step quadratic convergence of the MPRP method with a restart strategy.(English)Zbl 1221.65144

Unconstrained minimization of a continuously differentiable function $$f: \mathbb{R}^n\to\mathbb{R}$$ is considered. The authors investigate the convergence rate of the modified Polak-Ribière-Pólyak conjugate gradient method (further abbreviated MPRP method). They show that the $$r$$-step restart MPRP method (further abbreviated RMPRP method) with a special choice of the initial step-length with standard Armijo line-search, and under appropriate conditions will be globally convergent for uniformly convex objective functions. Further it is shown that under additional assumptions, $$n$$-step quadratic convergence can be proved. The results of numerical experiments presented in the concluding part of the paper support the theoretically derived convergence properties of the RMPRP method. Besides, the results show a good performance of the method in comparison with the MPRP method and some other methods published in the literature.

### MSC:

 65K05 Numerical mathematical programming methods

L-BFGS
Full Text:

### References:

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