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 ({tt 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.