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Numerical Algorithms
Published in: Numerical Algorithms 3/2021

21-04-2020 | Original Paper

Diagonal quasi-Newton methods via least change updating principle with weighted Frobenius norm

Authors: Wah June Leong, Sharareh Enshaei, Sie Long Kek

Published in: Numerical Algorithms | Issue 3/2021

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Abstract

This paper presents a class of low memory quasi-Newton methods with standard backtracking line search for large-scale unconstrained minimization. The methods are derived by means of least change updating technique analogous to that for the DFP method except that the full quasi-Newton matrix has been replaced by some diagonal matrix. We establish convergence properties for some particular members of the class under line search with Armijo condition. Sufficient conditions for the methods to be superlinearly convergent are also given. Numerical results are then presented to illustrate the usefulness of these methods in large-scale minimization.
previous article Asymptotically optimal quadrature rules for uniform splines over the real line
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Literature
1.
Andrei, N.: An unconstrained optimization test functions collection. J. Adv. Model Optim. 10, 147–161 (2008)MathSciNetMATH
2.
Bongartz, I., Conn, A.R., Gould, N.I.M., Toint, P. h. L.: CUTE: Constrained and unconstrained testing environment. ACM Trans. Math. Softw. 21, 123–160 (1995)CrossRef
3.
Broyden, C.G., Dennis, J.E., Moré, J.J.: On the local and superlinear convergence of quasi-Newton methods. J. Inst. Math. Appl. 12, 223–246 (1973)MathSciNetCrossRef
4.
Byrd, R.H., Nocedal, J., Yuan, Y.: Global convergence of a class of quasi-Newton methods on convex problems. SIAM J. Numer. Anal. 24, 1171–1190 (1987)MathSciNetCrossRef
5.
Dai, Y., Yuan, Y.: A nonlinear conjugate gradient method with a strong convergence property. SIAM J. Optim. 10, 177–182 (1999)MathSciNetCrossRef
6.
Dennis, J.E., Moré, J.J.: A characterization of superlinear convergence and its application to quasi-Newton methods. Math. Comp. 28, 549–560 (1974)MathSciNetCrossRef
7.
8.
Dolan, E., Moré, J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201–213 (2002)MathSciNetCrossRef
9.
10.
11.
Hager, W., Zhang, H.: A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim. 16, 170–192 (2005)MathSciNetCrossRef
12.
Hardy, G.H., Littlewood, J.E., Pòlya, G.: Inequalities, S2. Cambridge University Press, Cambridge (1988)MATH
13.
Hestenes, M.R., Stiefel, E.L.: Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. B 49, 409–432 (1952)MathSciNetCrossRef
14.
Khalfan, H., Byrd, R.H., Schnabel, R.B.: A theoretical and experimental study of the symmetric rank one update. SIAM J. Optim. 3, 1–24 (1993)MathSciNetCrossRef
15.
Li, J., Ying, J., Lu, B.: A flux-jump preserved gradient recovery technique for accurately predicting the electrostatics field of an immersed biomolecules. J. Comput. Phys. 396, 193–208 (2019)MathSciNetCrossRef
16.
Nazareth, J.L.: If quasi-Newton then why not quasi-Cauchy? SIAG/OPT Views-and-News 6, 11–14 (1995)
17.
Nazareth, J.L.: The quasi-Cauchy method: a stepping stone to derivative-free algorithms, Technical Report No. 95-3, Department of Pure and Applied Mathematics, Washington State University WA (1995)
18.
Oren, S.S., Luenberger, D.G.: Self-scaling variable metric (SSVM) algorithms, I: Criteria and sufficient conditions for scaling a class of algorithms. Manag. Sc. 20, 845–862 (1974)MathSciNetMATH
19.
Polak, B., Ribière, G.: Note surla convergence des méthodes de directions conjuguées. Rev. Francaise Infomat Recherche Operatonelle, 3e Année 16, 35–43 (1969)MATH
20.
Powell, M.J.D.: A new algorithm for unconstrained optimization. In: Rosen, J. B., Mangasarian, O. L., Ritter, K (eds.) Nonlinear Programming. Academic Press, New York (1970)
21.
Powell, M.J.D.: Some global convergence properties of a variable metric algorithm for minimization without exact line searches. In: Cottle, R.W., Lemke, C.E (eds.) Nonlinear Programming, SIAM-AMS Proceedings, pp 53–72. SIAM, Philadelphia (1976)
22.
Yuan, Y., Byrd, R.H.: Non-quasi-Newton updates for unconstrained optimization. J. Comput. Math. 13, 95–107 (1995)MathSciNetMATH
23.
Zhu, M., Nazareth, J.L., Wolkowicz, H.: The quasi-Cauchy relation and diagonal updating. SIAM J. Optim. 9, 1192–1204 (1999)MathSciNetCrossRef
Metadata
Title
Diagonal quasi-Newton methods via least change updating principle with weighted Frobenius norm
Authors
Wah June Leong
Sharareh Enshaei
Sie Long Kek
Publication date
21-04-2020
Publisher
Springer US
Published in
Numerical Algorithms / Issue 3/2021
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-00930-9

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