About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Vlček, Jan ; Lukšan, Ladislav
Modifications of the limited-memory BFGS method based on the idea of conjugate directions. (English). In: Chleboun, J., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 3-8, 2012. Institute of Mathematics AS CR, Prague, 2013. pp. 209-214
MSC: 65K05, 65Y20, 90C30, 90C53
Keywords:
limited-memory BFGS method; unconstrained optimization; quadratic objective function; convergence; performance
Summary:
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.
Partner of
EuDML logo