The global and superlinear convergence of a new nonmonotone MBFGS algorithm on convex objective functions

Journal of Computational and Applied Mathematics

Volumn 220, Issue 1-2, 2008, Pages 422-438

  Liu, Liying ^a   Yao, Shengwei ^b   Wei, Zengxin ^b  

^a LIAOCHENG UNIVERSITY   (China)

^b GUANGXI UNIVERSITY   (China)

Author keywords

Global convergence; MBFGS algorithm; Nonmonotone linesearch; Superlinear convergence; Unconstrained optimization

Indexed keywords

ALGORITHMS; BOOLEAN FUNCTIONS;

BFGS ALGORITHM; ELSEVIER (CO); NUMERICAL EXPERIMENTS; OBJECTIVE FUNCTION (OF); SUPERLINEAR CONVERGENCE; UNCONSTRAINED OPTIMIZATION;

FUNCTION EVALUATION;

EID: 47849115885     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2007.08.017     Document Type: Article

References (18)

1. Byrd R.H., Nocedal J., and Yuan Y. Global convergence of a class of quasi-Newton methods on convex problems. SIAM J. Numer. Anal. 24 (1987) 1171-1190
2. Dennis J.E., and Moré J.J. Quasi-Newton methods, motivation and theory. SIAM Rev. 19 (1977) 46-89
3. Griewank A., and Toint P.L. Local convergence analysis for partitioned quasi-Newton updates. Numer. Math. 39 (1982) 429-448
4. Grippo L., Lampariello F., and Lucidi S. A nonmonotone linesearch technique for Newton's methods. SIAM J. Numer. Anal. 23 (1986) 707-716
5. Guanghui L., and Jimen P. The convergence properties of a sort of nonmonotonic algorithm. J. Comput. Math. 1 (1992) 65-71
6. Guanghui L., and Jiye H. Global convergence of the variable metric algorithms with a generalized Wolfe linesearch (1993), Technical Report, No. 029, Institute of Applied Mathematics, Academia Sinica, Beijing, China
7. Guanghui L., Jiye H., and Defeng S. Global convergence of BFGS algorithm with nonmonotone linesearch. Optimization 34 (1995) 147-159
8. L. Guanghui, P. Jimen, A unified model of a variety of nonmonotonic linesearches, OR Decision Marking 1 616-618.
9. H. Jiye, L. Guanghui, General form of stepsize selection rule of linesearch and relevant analysis of global convergence of BFGS algorithm, Acta Math. Sinica (1992), to appear.
10. Jiye H., and Guanghui L. Notes on the general form of stepsize selection. OR and Decision Marking 1 (1992) 619-624
11. Jiye H., and Guanghui L. Global convergence analysis of a new nonmonotone BFGS algorithm on convex objective function. J. Comput. Optim. Appl. 7 (1997) 277-289
12. More J.J., Garbow B.S., and Hillstrome K.E. Testing unconstrained optimization software. ACM Trans. Math. Software 7 (1981) 17-41
13. Powell M.J.D. On the convergence of the variable metric algorithm. J. Inst. Math. Appl. 7 (1971) 21-36
14. Powell M.J.D. Some properties of the variable metric algorithm. In: Lootsman F.A. (Ed). Numerical Methods for Nonlinear Optimization (1972), Academia Press, London
15. M.J.D. Powell, Some global convergence properties of a variable metric algorithm for minimization without exact line searches, in: R.W. Cottle, C.E. Lemke, (Eds.), Nonlinear Programming, SIAM-AMS Proceedings, Vol. IX, American Mathematical Society, Providence, RI 1976, pp. 53-72.
16. Wei Z., Yu G., Yuan G., and Lian Zh. The superlinear convergence of a modified BFGS-type method for unconstrained optimization. Comput. Optim. Appl. 29 (2004) 315-332
17. Werner J. Uber die globale konvergenze von variable-metric verfahren mit nichtexakter schrittweitenbestimmung. Numer. Math. 31 (1978) 321-334
18. Zhang Y., and Tewarson P.R. Quasi-Newton algorithm with updates from the preconvex part of Broyden's family. SIAM J. Numer. Anal 8 (1988) 487-509