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.
@article{702729,
title = {Modifications of the limited-memory BFGS method based on the idea of conjugate directions},
booktitle = {Programs and Algorithms of Numerical Mathematics},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2013},
pages = {209-214},
url = {http://dml.mathdoc.fr/item/702729}
}
Vlček, Jan; Lukšan, Ladislav. Modifications of the limited-memory BFGS method based on the idea of conjugate directions, dans Programs and Algorithms of Numerical Mathematics, GDML_Books, (2013), pp. 209-214. http://gdmltest.u-ga.fr/item/702729/