Global Convergence of Algorithms with Nonmonotone Line Search Strategy in Unconstrained Optimization

Results in Mathematics

Volumn 41, Issue 3-4, 2002, Pages 320-333

  Hüther, Björn ^a  

^a Dipl Math Björn Hüther   (Germany)

Author keywords

49M37; 65K05; 90C30; BFGS method; global convergence; Nonmonotone line search strategy

Indexed keywords

EID: 33646236888     PISSN: 14226383     EISSN: 14209012     Source Type: Journal    
DOI: 10.1007/BF03322774     Document Type: Article

References (22)

1. L. Grippo, F. Lampariello, S. Lucidi (1986), A nonmonotone line search technique for Newton’s method, SIAM Journal on Numerical Analysis 23, 707–716.
2. L. Armijo (1966), Minimization of functions having Lipschitz continuous first partial derivatives, Pacific Journal of Mathematics 16, 1–3.
3. H. H. Rosenbrock(1960), An automatic method for finding the greatest or least value of a function, The Computer Journal 3, 175–184.
4. G. H. Liu, L. L. Jing (2000), Convergence of the nonmonotone Perry and Shanno method for optimization, Computational Optimization and Applications 16, 159–172.
5. G. H. Liu, L. L. Jing, L. X. Han, D. Han (1999), A class of nonmonotone conjugate gradient methods for unconstrained optimization, Journal of Optimization Theory and Applications 101, 127–140.
6. S. Lucidi, M. Roma (1994), Nonmonotone conjugate gradient methods for optimization, in: J. Henry, J.-P. Yvon, eds., System Modelling and Optimization, Lecture Notes in Control and Information Sciences 197, Springer-Verlag, London; Berlin; Heidelberg; New York, 206–214.
7. M. Al-Baali (1985), Descent property and global convergence of the Fletcher-Reeves method with inexact line search, IMA Journal of Numerical Analysis 5, 121–124.
8. Ph. Wolfe (1969), Convergence conditions for ascent methods, SIAM Review 11, 226–235.
9. J. Y. Han, G. H. Liu (1997), Global convergence analysis of a new nonmonotone BFGS algorithm on convex objective functions, Computational Optimization and Applications 7, 277–289.
10. G. H. Liu, J. Y. Han, D. F. Sun (1995), Global convergence of the BFGS algorithm with nonmonotone linesearch, Optimization 34, 147–159.
11. B. Hüther (1999), Nichtmonotone Schrittweiten bei unrestringierten Optimierungsaufgaben, Diplomarbeit, Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Germany.
12. L. Grippo, F. Lampariello, S. Lucidi (1991), A class of nonmonotone stabilization methods in unconstrained optimization, Numerische Mathematik 59, 779–805.
13. Ph. L. Toint (1996), An assessment of nonmonotone linesearch techniques for unconstrained optimization, SIAM Journal on Scientific Computing 17, 725–739.
14. W. Warth, J. Werner (1977), Effiziente Schrittweitenfunktionen bei unrestringierten Optimierungsaufgaben, Computing 19, 59–72.
15. J. Werner (1992), Numerische Mathematik 2, Friedr. Vieweg & Sohn, Braunschweig; Wiesbaden.
16. J. Werner (1978), Über die globale Konvergenz von Variable-Metrik-Verfahren mit nicht-exakter Schrittweitenbestimmung, Numerische Mathematik 31, 321–334.
17. P. Kosmol (1989), Methoden zur numerischen Behandlung nichtlinearer Gleichungen und Optimierungsaufgaben, B. G. Teubner, Stuttgart.
18. G. Zoutendijk (1970), Nonlinear programming, computational methods, in: J. Abadie, ed., Integer and Nonlinear Programming, North-Holland Publishing Company, Amsterdam; London, 37–86.
19. J. Werner (1989), Global convergence of quasi-Newton methods with practical line searches, NAM-Bericht 67, Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Germany.
20. R. Fletcher (1970), A new approach to variable metric algorithms, The Computer Journal 13, 317–322.
21. J. D. Pearson (1969), Variable metric methods of minimisation, The Computer Journal 12, 171–178.
22. M. J. D. Powell (1971), On the convergence of the variable metric algorithm, Journal of the Institute of Mathematics and its Applications 7, 21–36.