Recursive form of general limited memory variable metric methods

Lukšan, Ladislav, and Vlček, Jan. "Recursive form of general limited memory variable metric methods." Kybernetika 49.2 (2013): 224-235. <http://eudml.org/doc/260574>.

@article{Lukšan2013,
abstract = {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.},
author = {Lukšan, Ladislav, Vlček, Jan},
journal = {Kybernetika},
keywords = {unconstrained optimization; large scale optimization; limited memory methods; variable metric updates; recursive matrix formulation; algorithms; unconstrained optimization; large scale optimization; limited memory methods; variable metric updates; recursive matrix formulation; algorithms},
language = {eng},
number = {2},
pages = {224-235},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Recursive form of general limited memory variable metric methods},
url = {http://eudml.org/doc/260574},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Lukšan, Ladislav
AU - Vlček, Jan
TI - Recursive form of general limited memory variable metric methods
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 2
SP - 224
EP - 235
AB - 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.
LA - eng
KW - unconstrained optimization; large scale optimization; limited memory methods; variable metric updates; recursive matrix formulation; algorithms; unconstrained optimization; large scale optimization; limited memory methods; variable metric updates; recursive matrix formulation; algorithms
UR - http://eudml.org/doc/260574
ER -