New Hybrid Conjugate Gradient Method as a Convex Combination of LS and CD methods

Abstract

A new hybrid conjugate gradient algorithm is
considered. The conjugate gradient pa\-ra\-me\-ter $\beta_k$ is computed as a convex
combination of $\beta_k^{CD}$ and $\beta_k^{LS}$. The parameter $\theta_k$ is computed in such
a way that the conjugacy condition is satisfied.% independently of
%the line search.

The strong Wolfe line search conditions are used.

Numerical comparisons show that the present hybrid conjugate
gra\-dient algorithm often behaves better than some known algorithms.