Another nonlinear conjugate gradient algorithm for unconstrained optimization
A nonlinear conjugate gradient algorithm which is a modification of the Dai and 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 parameterized sufficient descent condition with a parameter delta(k) is proposed. The parameter delta(k) is computed by means of the conjugacy condition, thus an algorithm which is a positive multiplicative modification of the Hestenes and Stiefel [Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards Sec. B 48 (1952). pp. 409-436] algorithm is obtained. The algorithm can be viewed as an adaptive version of the Dai and 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 [A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim. 16 (2005), pp. 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.
unconstrained optimization conjugate gradient method sufficient descent condition conjugacy condition numerical comparisons