Geodesic
Recursive form of general limited memory variable metric methods
Kybernetika, Tome 49 (2013) no. 2, pp. 224-235 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this report we propose a new recursive matrix formulation of limited memory variable metric methods. This approach can be used for an arbitrary update from the Broyden class (and some other updates) and also for the approximation of both the Hessian matrix and its inverse. The new recursive formulation requires approximately $4 m n$ multiplications and additions per iteration, so it is comparable with other efficient limited memory variable metric methods. Numerical experiments concerning Algorithm 1, proposed in this report, confirm its practical efficiency.
In this report we propose a new recursive matrix formulation of limited memory variable metric methods. This approach can be used for an arbitrary update from the Broyden class (and some other updates) and also for the approximation of both the Hessian matrix and its inverse. The new recursive formulation requires approximately $4 m n$ multiplications and additions per iteration, so it is comparable with other efficient limited memory variable metric methods. Numerical experiments concerning Algorithm 1, proposed in this report, confirm its practical efficiency.
Classification : 49K35, 49M30, 90C06, 90C26, 90C47, 90C51, 90C53
Keywords: unconstrained optimization; large scale optimization; limited memory methods; variable metric updates; recursive matrix formulation; algorithms 
@article{KYB_2013_49_2_a2,
     author = {Luk\v{s}an, Ladislav and Vl\v{c}ek, Jan},
     title = {Recursive form of general limited memory variable metric methods},
     journal = {Kybernetika},
     pages = {224--235},
     year = {2013},
     volume = {49},
     number = {2},
     mrnumber = {3085394},
     zbl = {1266.49060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013_49_2_a2/}
}
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Lukšan, Ladislav; Vlček, Jan. Recursive form of general limited memory variable metric methods. Kybernetika, Tome 49 (2013) no. 2, pp. 224-235. http://geodesic.mathdoc.fr/item/KYB_2013_49_2_a2/