Modified Liu–Storey Type Nonlinear Conjugate Gradient Method for Large-Scale Unconstrained Optimization

Motivated by the idea of Li and Fukushima, we propose a new Liu–Storey (LS) type conjugate gradient formula β ^VLS _k for computing unconstrained optimization problems. It's form is similar to the original LS formula and it inherits all nice properties of the LS method. By utilizing the technique of the three-term PRP method in Zhang, Zhou, and Li, we propose a modified Liu–Storey (LS) type method which can generate sufficient descent directions. We obtain the global convergence with standard Armijio line search. Moreover, under appropriate conditions, the linear convergence rate of the modified method is established. The numerical results show that the pro-posed method is efficient.