Global Convergence Analysis of a New Nonmonotone BFGS Algorithm on Convex Objective Functions *

Computational Optimization and Applications

Volumn 7, Issue 3, 1997, Pages 277-289

  Han, Jiye ^a   Liu, Guanghui ^b  

^a INSTITUTE OF APPLIED MATHEMATICS   (China)

^b Northwestern University   (United States)

Author keywords

BFGS algorithm; Global convergence; Nonmonotone linesearch; Unconstrained optimization

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; MATRIX ALGEBRA; OPTIMIZATION; PROBLEM SOLVING;

GLOBAL CONVERGENCE; NONMONOTONE LINE RESEARCH; UNCONSTRAINED OPTIMIZATION;

ALGORITHMS;

EID: 0031143392     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008656711925     Document Type: Article

References (19)

1. R.H. Byrd, "If BFGS converges, it converges fast," manuscript, 1989.
2. R.H. Byrd and J. Nocedal, "A tool for the analysis of quasi-Newton methods with application to unconstrained minimization," SIAM J. Numer. Anal., vol. 26, pp. 727-739, 1989.
3. R.H. Byrd, J. Nocedal, and Y. Yuan, "Global convergence of a class of quasi-Newton methods on convex problems," SIAM J. Numer. Anal., vol. 24, pp. 1171-1189, 1987.
4. J.C. Gilbert and J. Nocedal, "Global convergence properties of conjugate gradient methods for optimization," SIAM J. Optimization, vol. 2, no. 1, pp. 21-42, 1992.
5. L. Grippo, F. Lampariello, and S. Lucidi, "A nonmonotone linesearch technique for Newton's methods," SIAM J. Numer. Anal., vol. 23, pp. 707-716, 1986.
6. Han Jiye and Liu Guanghui, "General form of stepsize selection rule of linesearch and relevant analysis of global convergence of BFGS algorithm," to appear in Acta Mathematicae Applicatae Sinica, 1992.
7. Han Jiye and Liu Guanghui, "Notes on the general form of stepsize selection," OR and Decision Making, vol. I, pp. 619-624, 1992.
8. Liu Guanghui, Han Jiye, and Sun Defeng, "Global convergence of the BFGS algorithm with nonmonotone linesearch," Optimization, vol. 34, pp. 147-159, 1995.
9. Liu Guanghui and Han Jiye, "Global convergence of the variable metric algorithms with a generalized Wolfe linesearch," Technical Report, Institute of Applied Mathematics, Academia Sinica, Beijing, China, no. 029, 1993 (to be published in J. of Mathematical Research and Exposition).
10. Liu Guanghui and Peng Jimen, "A unified model of a variety of nonmonotonic linesearches," OR and Decision Making, vol. I, pp. 616-618.
11. Liu Guanghui and Peng Jimen, "The convergence properties of a sort of nonmonotonic algorithm," J. of Computation Mathematics, vol. 1, pp. 65-71, 1992.
12. J. Nocedal, "Theory of algorithms for unconstrained optimization," Acta Numerica, pp. 1-36, 1991.
13. J. Nocedal and C. Zhu, "Test driver for BFGS," Optimization Technology Center, 1995.
14. J.D. Pearson, "Variable metric methods of minimization," The Computer J., vol. 12, pp. 171-178, 1969.
15. M.J.D. Powell, "On the Convergence of the variable metric algorithm," J. of the Institute of Mathematics and its Applications, vol. 7, pp. 21-36, 1971.
16. M.J.D. Powell, "Some properties of the variable metric algorithm," in F.A. Lootsma, (Ed.), Numerical Methods for Nonlinear Optimization, Academia Press: London, 1972.
17. M.J.D. Powell, "Some global convergence properties of a variable metric algorithm for minimization without exact linesearches," in Nonlinear Programming, SIAM-AMS Proceedings, R. W. Cottle and C.E. Lemke (Eds.), vol. IX., American Mathematical Society, Providence, RI, 1976.
18. J. Werner, "Über die Globale Konvergenze von variable-metric verfahren mit nichtexakter schrittweitenbestimmung," Numer. Math., vol. 31, pp. 321-334, 1978.
19. J. Werner, "Global convergence of quasi-Newton methods with practical linesearches," Technical Report, NAM-Bericht Nr. 67, Marz, 1989.