Another nonlinear conjugate gradient algorithm for unconstrained optimization

A nonlinear conjugate gradient algorithm which is a modification of the Dai and Yuan [Y.H. Dai and Y, Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim., 10 (1999), pp.177-182.] conjugate gradient algorithm satisfying a parametrized sufficient descent condition with a parameter k δ is proposed. The parameter k δ is computed by means of the conjugacy condition, thus an algorithm which is a positive multiplicative modification of the Hestenes and Stiefel [M.R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Research Nat. Bur. Standards Sec. B. 48, pp. 409-436, 1952.] algorithm is obtained. The algorithm can be viewed as an adaptive version of the Dai and Liao [Y.H. Dai and L.Z. Liao, New conjugacy conditions and related nonlinear conjugate gradient methods. Appl. Math. Optim., 43 (2001), pp. 87-101.] conjugate gradient algorithm. Close to our computational scheme is the conjugate gradient algorithm recently proposed by Hager and Zhang [W.W. Hager and H. Zhang, A new conjugate gradient method with guaranteed descent and an efficient line search, SIAM Journal on Optimization, 16 (2005), 170-192.]. Computational results, for a set consisting of 750 unconstrained optimization test problems, show that this new conjugate gradient algorithm substantially outperforms the known conjugate gradient algorithms.