Modifications of the limited-memory BFGS method based on the idea of conjugate directions

0390286 - ÚI 2013 RIV CZ eng K - Conference Paper (Czech conference)
Vlček, Jan - Lukšan, Ladislav
Modifications of the limited-memory BFGS method based on the idea of conjugate directions.
Programs and Algorithms of Numerical Matematics 16. Prague: Institute of Mathematics, Academy of Sciences of the Czech Republic, 2013 - (Chleboun, J.; Segeth, K.; Šístek, J.; Vejchodský, T.), s. 209-214. ISBN 978-80-85823-62-2.
[Programy a algoritmy numerické matematiky /16./. Dolní Maxov (CZ), 03.06.2012-08.06.2012]
Institutional support: RVO:67985807
Keywords : limited memory * variable metric methods * conjugate directions * large scale optimization * numerical solution
Subject RIV: BA - General Mathematics
http://users.math.cas.cz/~panm/Panm16/proceedings_final/209_vlcek.pdf

Simple modifications of the limited-memory BFGS method (L-BFGS) for large scale unconstrained optimization are considered, which consist in corrections of the used difference vectors (derived from the idea of conjugate directions), utilizing information from the preceding iteration. For quadratic objective functions, the improvement of convergence is the best one in some sense and all stored difference vectors are conjugate for unit stepsizes. The algorithm is globally convergent for convex sufficiently smooth functions. Numerical experiments indicate that the new method often improves the L-BFGS method significantly.
Permanent Link: http://hdl.handle.net/11104/0219149