- Free Articles
-
Reactive Scheduling of Batch Processes
Encyclopedia of Optimization
-
Variational methods in shape analysis
Handbook of Mathematical Methods in Imaging
-
History of Geomathematics: Navigation on Sea
Handbook of Geomathematics
-
Geomagnetic Field: Satellite Data
Handbook of Geomathematics
-
From Omnipotent to Omnipresent Maps
Handbook of Geomathematics
- More Free Articles
Mathematics and Statistics
>
Encyclopedia of Optimization
>
Broyden Family of Methods and the BFGS Update: BFM
This is the free portion of the full article.
The full article
is available to licensed users only.
How do I get access?
Broyden Family of Methods and the BFGS Update
Article Outline
Keywords
See also
References
Keywords Unconstrained optimization - BFGS update - DFP update - Broyden family of methods - Rank-two updates - Quasi-Newton methods
Quasi-Newton methods attempt to update a Hessian approximation (or the inverse of it) instead of evaluating the Hessian matrix exactly at each iteration, as in the basic Newton method for unconstrained optimization . Consider the optimization problem:
 |
For this problem the Newton method requires the solution and updating iteratively of the solution point according to:
where H(x (k)) denotes the Hessian matrix at point x (k) (kth iteration of Newton's method), g(x (k)) is the gradient vector at the same point, and finally ∆x (k) is the correction to the point x (k). The correction is applied according to:
where for
 |
(1) |
 |