On the asymptotic behaviour of some new gradient methods

Mathematical Programming

Volumn 103, Issue 3, 2005, Pages 541-559

  Dai, Yu Hong ^a   Fletcher, Roger ^b  

^a CHINESE ACADEMY OF SCIENCES   (China)

^b UNIVERSITY OF DUNDEE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; OPTIMIZATION; PROBLEM SOLVING; VECTORS;

BARZILAI-BORWEIN (BB) GRADIENT METHOD; CONJUGATE GRADIENT METHODS; EIGENCOMPONENTS; QUADRATIC FUNCTIONS;

GRADIENT METHODS;

EID: 21644488546     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-004-0516-9     Document Type: Article

References (19)

1. Akaike, H.: On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method. Ann. Inst. Statist. Math. Tokyo 11, 1-17 (1959)
2. Birgin, E.G., Chambouleyron, I., Martínez, J.M.: Estimation of the optical constants and the thickness of thin films using unconstrained optimization. J. Comput. Phys. 151, 862-880 (1999)
3. Birgin, E.G., Evtushenko, Y.G.: Automatic differentiation and spectral projected gradient methods for optimal control problems. Optim. Meth. Softw. 10, 125-146 (1998)
4. Birgin, E.G., Martínez, J.M., Raydan, M.: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10, 1196-1211 (2000)
5. Barzilai, J. Borwein, J.M.: Two-point step size gradient methods. IMA J. Numer. Anal. 8, 141-148 (1988)
6. Cauchy, A.: Méthode générale pour la résolution des systèms d'équations simultanées. Comp. Rend. Sci. Paris 25, 536-538 (1847)
7. Dai, Y.H.: Alternate Step Gradient Method. Research report. State Key laboratory of Scientific and Engineering Computing. Institute of Computational Mathematics and Scientific/Engineering computing. Academy of Mathematics and System Sciences. Chinese Academy of Sciences. 2001
8. Dai, Y.H., Liao, L.-Z.: R - linear convergence of the Barzilai and Borwein gradient method. IMA J. Numer. Anal. 26, 1-10 (2002)
9. Fletcher, R.: Low storage methods for unconstrained optimization. Lect. Appl. Math. (AMS)26, 165-179 (1999)
10. Fletcher, R.: On the Barzilai-Borwein Method. Research report. Department of Mathematics. University of Dundee, 2001
11. Friedlander, A., Martínez, J.M., Molina, B., Raydan, M.: Gradient method with retards and generalizations. SIAM J. Numer. Anal. 36, 275-289 (1999)
12. Glunt, W., Hayden, T.L., Raydan, M.: Molecular conformations from distance matrices. J. Comput. Chem. 14, 114-120 (1993)
13. Grippo, L., Lampariello, F., Lucidi, S.: A nonmonotone line search technique for Newton's method. SIAM J. Numer. Anal. 23, 707-716 (1986)
14. Liu, W.B., Dai, Y.H.: Minimization Algorithms Based on Supervisor and Searcher Cooperation: J. Optim. Theor. Appl. 111, 359-379 (2001)
15. Nocedal, J., Sartentaer, A., Zhu, C.: On the Behavior of the Gradient Norm in the Steepest Descent Method. Comput. Optim. Appl. 22, 5-35 (2002)
16. Raydan, M.: On the Barzilai and Borwin choice of steplength for the gradient method. IMA J. Numer. Anal. 13, 321-326 (1993)
17. Raydan, M.: The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM J. Optim. 7, 26-33 (1997)
18. Raydan, M.: Nonmonotone spectral methods for large-scale nonlinear systems. Report in the International Workshop on "Optimization and Control with Applications", Erice, Italy, July 9-17, 2001
19. Raydan, M., Svaiter, B.F.: Relaxed Steepest Descent and Cauchy-Barzilai-Borwein Method. Comput. Optim. Appl. 21, 155-167 (2002)