Broyden-Fletcher-Goldfarb-Shanno method

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. 

To circumvent this calculation, Powell (1977) used the Broyden, Fletcher, Goldfarb, Shanno (BFGS) quasi-Newton method to approximate X . This saves con-... 

D. K. Agrafiotis and H. S. Rzepa, /. Chem. Res. (S), 100 (1988). Evaluation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) Variable Metric Method in Geometry Optimisation Using Semi-Empirical SCF-MO Procedures. 

By utilizing forces on FES, we can identify the SS and TS stmctures in solution with full optimization with respect to all coordinates of the solute molecules. For example, if we adopt the quasi-Newton method with the following Broyden-Fletcher-Goldfarb-Shanno (BFGS) procedure [26-29] for stractural optimization scheme in the FEG method, the i -F l)-th reactant structure is taken as,... 

Various update methods carry the names of Broyden, Davidon, Fletcher, Goldfarb, Powell, and Shanno, in different combinations. We recommend a comprehensive textbook, namely... 

There are several other methods for updating Dj in step 5. Another important method is based on the BFGS formula, which was developed by Broyden (1970), Fletcher (1970), Goldfarb (1970), and Shanno (1970) and is given by... 

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