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Abstract: The Barzilai-Borwein (BB) gradient method, and some other new gradient methods have shown themselves to be competitive with conjugate gradient methods for solving large dimension nonlinear unconstrained optimization problems. Little is known about the asymptotic behaviour, even when applied to n dimensional quadratic functions, except in the case that n = 2. We show in the quadratic case how it is possible to compute this asymptotic behaviour, and observe that as n increases there is a... (Update)
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BibTeX entry: (Update)
@misc{ dai-asymptotic,
author = "Yu-Hong Dai and Roger Fletcher",
title = "On the Asymptotic Behaviour of some New Gradient Methods",
url = "citeseer.ist.psu.edu/dai03asymptotic.html" }
Citations (may not include all citations):58 A nonmonotone line search technique for Newton's method (context) - Grippo, Lampariello et al. - 1986
27 Two-point step size gradient methods (context) - Barzilai, Borwein - 1988
25 Molecular conformations from distance matrices (context) - Glunt, Hayden et al. - 1993
24 The Barzilai and Borwein gradient method for the large scale.. (context) - Raydan - 1997
24 Nonmonotone spectral projected gradient methods on convex se.. - Birgin, Mart et al. - 2000
20 the Barzilai and Borwein choice of steplength for the gradie.. (context) - Raydan - 1993
14 Estimation of the optical constants and the thickness of thi.. - Birgin, Chambouleyron et al. - 1999
11 a successive transformation of probability distribution and .. (context) - Akaike - 1959
7 Low storage methods for unconstrained optimization (context) - Fletcher - 1999
7 Gradient method with retards and generalizations - Friedlander, Mart et al. - 1999
4 erentiation and spectral projected gradient methods for opti.. (context) - Birgin, Evtushenko et al. - 1998
4 linear convergence of the Barzilai and Borwein gradient meth.. (context) - Dai, Liao - 2002
3 the Barzilai-Borwein Method - Fletcher - 2001
2 erale pour la resolution des systems d'equations simultan.. (context) - Cauchy, ethode et al.
1 the Behavior of the Gradient Norm in the Steepest Descent Me.. - Nocedal, Sartentaer et al. - 2002
1 State Key Laboratory of Scienti c and Engineering Computing (context) - Dai, Gradient et al. - 2001
1 Minimization Algorithms Based on Supervisor and Searcher Coo.. (context) - Liu, Dai - 2001
1 Nonmonotone spectral methods for large-scale nonlinear syste.. (context) - Raydan - 2001
1 Relaxed Steepest Descent and Cauchy-BarzilaiBorwein Method (context) - Raydan, Svaiter - 2002
Documents on the same site (http://www.maths.dundee.ac.uk/~fletcher/):
Dense Factors of Sparse Matrices - Fletcher (1997) (Correct)
Nonlinear Programming without a penalty function - Fletcher, Leyffer (2000) (Correct)
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