Recursive form of general limited memory variable metric methods

0381993 - ÚI 2014 RIV CZ eng J - Journal Article
Lukšan, Ladislav - Vlček, Jan
Recursive form of general limited memory variable metric methods.
Kybernetika. Roč. 49, č. 2 (2013), s. 224-235. ISSN 0023-5954
Institutional support: RVO:67985807
Keywords : unconstrained optimization * large scale optimization * limited memory methods * variable metric updates * recursive matrix formulation * algorithms
Subject RIV: BA - General Mathematics
Impact factor: 0.563, year: 2013
http://dml.cz/handle/10338.dmlcz/143365

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.
Permanent Link: http://hdl.handle.net/11104/0212341