Abstract

EXPERIMENTAL STUDY OF THE BROYDEN CLASS UPDATING METHOD FOR SOLVING NON-LINEAR UNCONSTRAINED OPTIMIZATION PROBLEMS

B. I. Oruh,1 B. O. Osu2 and M. K. Ahamefule3

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The main purpose of this paper is to seek for a suitable combination of the most successful updates-the DFP and the BFGS-and use the combined updates in solving Non-Linear optimization problems. This combined updates belongs to what is referred to in literature as the Broyden updates which is family of quasi Newton methods that depend on a real valued parameter. Its Hessian approximation update formula is where stands for the update obtained by the Broyden Fletcher Goldfarb Shanno (BFGS) method, for the update of the Davidon Fletcher Powell (DFP) method and ??R. The simulation results shows that as ??0 both the average time for execution and number of iterations reduces. The value ?=0.3 is thus recommended as a suitable value for the parameter ? in the convex combination of the BFGS and DFP to enhance the convergence of the quasi-Newton method. Keywords: Broyden class updating technique, DFP, BFGS, convex combination.

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