Global convergence of the Fletcher-Reeves algorithm with inexact linesearch. (English) Zbl 0834.90122

Summary: We investigate the convergence properties of the Fletcher-Reeves algorithm. Under conditions weaker than those in a paper of M. Al-Baali, we get the global convergence of the Fletcher-Reeves algorithm with a low-accuracy inexact linesearch.


90C30 Nonlinear programming
Full Text: DOI


[1] Al-Baali, M., Descent property and global convergence of the Fletcher-Reeves method with inexact linesearch,IMA Numer. Anal.,5 (1985), 121–124. · Zbl 0578.65063
[2] Cloutier, J.R. and Wilson, R.F., Periodically preconditioned congate-restoration algorithms,J. Optim. theory Appl.,70 (1991), 79–95. · Zbl 0737.90061
[3] Cohan, A., Rate of convergence of several conjugate gradient algorithms,SIAM J. Numer. Anal.,9 (1972), 248–259. · Zbl 0279.65051
[4] Dixon, L.C.W., Duksbury, P.G. and Singh, P., A new three-term conjugate gradient method, Technical Report No. 130, Numerical Optimization Centre, Hatfield Polytechnic, Hatfield, Hertford Shire, England, 1985. · Zbl 0556.90077
[5] Fletcher, R. and Reeves, C.M., Function minimization by conjugate gradients,Comput. J.,7 (1964), 149–154. · Zbl 0132.11701
[6] Hayami, K. and Harada, N.,On the effectiveness of the diagonally scaled conjugate gradient algorithm on vector computers, Trans. Inform. Process. Soc. Japan,30 (1989), 1164–1375.
[7] Liu, Y. and Storey, C., Eficient generalized gradient algorithm I: Theory,J. Optim. Theory Appl.,69 (1991), 129–137. · Zbl 0724.90067
[8] Nazareth, J.L., Conjugate gradient methods less dependent on conjugacy,SIAM Rev.,28 (1986), 501–511. · Zbl 0625.90077
[9] Powell, M.J.D., Nonconvex minimization calculations and the conjugate gradient method, in: Numerical Analysis (Griffiths, D.F., ed.), Dundee, 1983, pp. 122–141.
[10] Shanno, D.F., Global convergent conjugate gradient algorithms,Math. Programming,33 (1985), 61–67 · Zbl 0579.90079
[11] Touati-Ahmed, D. and Storey, C., Efficient hybird conjugate gradient techniques,J. Optim. Theory Appl.,64 (1990), 379–397. · Zbl 0687.90081
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.