A New Hybrid Conjugate Gradient Method Based on Eigenvalue Analysis for Unconstrained Optimization Problems

In this paper, two extended three-term conjugate gradient methods based on the Liu-Storey (LS) conjugate gradient method are presented to solve unconstrained optimization problems. A remarkable property of the proposed methods is that the search direction always satisfies the sufficient descent condition independent of line search method, based on eigenvalue analysis. The global convergence of proposed algorithms is established under suitable conditions. Preliminary numerical results show that the proposed methods are efficient and robust to solve the unconstrained optimization problems..