Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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Hessians are needed and will be approximated by secant updates (BFGS or SR1) from a series of gradient evaluations


Alias: none

Argument(s): none

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
(Choose One)
Group 1 bfgs Use BFGS method to compute quasi-hessians
sr1 Use the Symmetric Rank 1 update method to compute quasi-Hessians


The quasi_hessians specification means that Hessian information is needed and will be approximated using secant updates (sometimes called "quasi-Newton updates", though any algorithm that approximates Newton's method is a quasi-Newton method).

Compared to finite difference numerical Hessians, secant approximations do not expend additional function evaluations in estimating all of the second-order information for every point of interest. Rather, they accumulate approximate curvature information over time using the existing gradient evaluations.

The supported secant approximations include the Broyden-Fletcher-Goldfarb-Shanno (BFGS) update (specified with the keyword bfgs) and the Symmetric Rank 1 (SR1) update (specified with the keyword sr1).

See Also

These keywords may also be of interest: