Broyden-Fletcher-Goldfarb-Shanno

It is often desirable that the approximate Hessian is positive definite so that the quadratic model has a minimum. To ensure this we may use the Broyden-Fletcher-Goldfarb-Shanno (BFGS) update given by... 

A modified version of the deMon DFT code [38] in which molecular orbitals are given as linear combinations of Gaussian-type atomic functions was used for the PWP computations. In order to localise the extreme points on the potential energy surfaces the Broyden-Fletcher-Goldfarb-Shanno minimisation algorithm [39]... 

The methods differ in the formula used to generate the sequence S, k=0,l,2,., and after Fletcher and Powell s 3 analysis of Davidon s method a whole spate of formulae were invented in the sixties. Broyden 4 introduced some rationalization by identifying a one-parameter family, and recommended a particular member, now commonly referred to as the BFGS (Broyden-Fletcher-Goldfarb-Shanno) formula. Huang 5 widened the family, but by the end of the sixties numerical experience was producing a consensus that the BFGS formula was the most robust of the formulae available. The formula is... 

Any quasi-Newton method for the minimization of E can be applied. We use the Broyden-Fletcher-Goldfarb-Shanno [24] procedure. 

J. D. Head and M. C. Zerner, Chon. Phys. h-ll., 122, 264 (1985). A Broyden-Fletcher-Goldfarb-Shanno Optimiz.arion Procedure for Molecular Geometries. 

There are three Hessian matrix elements to be solved for, but only two equations to be satisfied, so there is not a unique solution for the and several recipes have been proposed to find improved that satisfy (15.73). One commonly used recipe is the Broyden, Fletcher, Goldfarb, Shanno (BFGS) procedure Leach, p. 229). 

BFGS Broyden Fletcher Goldfarb Shanno algorithm, an iterative metho for solving unconstrained nonlinear optimization problems ... 

The Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm ... 

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