FUNCTION MINIMIZATION BY VARIANTS OF BFGS-CG METHOD

Abstract

 Some variants of Broyden-Fletcher-Goldfarb-Shanno conjugate gradient (BFGS-CG) method are developed in this work. This is achieved by combining BFGS method with coefficients of CG like Fletcher-Reeves, HestenesStiefel, Dai and Yuan, etc. We prove the global convergence of one of these methods using Armijo-type line search. The purpose of this paper is to present these algorithms as well as their Dolan and More's performances to solve variety of large-scale unconstrained optimization problems. Some comparisons with conventional BFGSCG algorithm are also presented.

Preliminary results show that among the variants of BFGS – CG method, BFGS – BAN competes well with the conventional BFGS – CG method in terms of number of iterations and CPU time.