Vol. LXXVIII, 2 (2009)
p. 173 - 181

Quasi-Newton type of diagonal updating for the L-BFGS method

M. L. Sahari and R. Khaldi

Received: February 5, 2007;   Revised: May 5, 2009;   Accepted: May 11, 2009

Abstract.   The use of the L-BFGS method is very efficient for the resolution of large scale optimization problems. The techniques to update the diagonal matrix seem to play an important role in the performance of overall method. In this work, we introduce some methods for updating the diagonal matrix derived from quasi-Newton formulas (DFP, BFGS). We compare their performances with the Oren-Spedicato update proposed by Liu and Nocedal (1989) and we get considerable amelioration in the total running time. We also study the convergence of L-BFGS method if we use the BFGS and inverse BFGS update of the diagonal matrix on uniformly convex problems. 

Keywords:  nonlinear unconstrained optimization; Quasi-Newton; BFGS; L-BFGS; line search.  

AMS Subject classification: Primary:  65K05, 65K10, 90C30.  

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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

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