Broyden-Fletcher-Goldfarb-Shanno algorithm

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

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

Structures were fully optimized, within symmetry constraints, using a Broyden-Fletcher-Goldfarb-Shanno (BFGS) [7] algorithm. Optimization was considered to be complete when the residual forces were below 1.0 x 10 " Hartrees Bohr V The... 

The inverse of the Hessian matrix is approximated by a symmetric positive definite matrix that is constructed iteratively. To that end, the Scilab function optim () [10] uses the Broyden, Fletcher, Goldfarb and Shanno (BFGS) update [11], Alternatively, the Levenberg-Marquardt algorithm implemented in the Scilab function IsqrsolveO may be used. 

One of the most efficient and widely used updating formula is the BFGS update. Broyden (1970), Fletcher (1970), Goldfarb (1970), and Shanno (1970) independently published this algorithm in the same year, hence the combined name BFGS. Here the approximate Hessian is given by... 

The BFGS (Broyden [42], Fletcher [124], Goldfarb [145], Shanno [379]) algorithm is an update procedure for the Hessian matrix that is widely used in iterative optimization [125]. The simpler Rm update takes the form... 

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