Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Trustregion method for nonlinear least squares
This keyword is related to the topics:
Alias: none
Argument(s): none
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Optional  function_precision  Specify the maximum precision of the analysis code responses  
Optional  absolute_conv_tol  Absolute convergence tolerance  
Optional  x_conv_tol  Xconvergence tolerance  
Optional  singular_conv_tol  Singular convergence tolerance  
Optional  singular_radius  Singular radius  
Optional  false_conv_tol  False convergence tolerance  
Optional  initial_trust_radius  Initial trust region radius  
Optional  covariance  Determine how the final covariance matrix is computed  
Optional  regression_diagnostics  Turn on regression diagnostics  
Optional  convergence_tolerance  Stopping criterion based on convergence of the objective function or statistics  
Optional  max_iterations  Stopping criterion based on number of iterations  
Optional  speculative  Compute speculative gradients  
Optional  max_function_evaluations  Stopping criteria based on number of function evaluations  
Optional  scaling  Turn on scaling for variables, responses, and constraints  
Optional  model_pointer  Identifier for model block to be used by a method 
NL2SOL is available as nl2sol
and addresses unconstrained and boundconstrained least squares problems. It uses a trustregion method (and thus can be viewed as a generalization of the LevenbergMarquardt algorithm) and adaptively chooses between two Hessian approximations, the GaussNewton approximation alone and the GaussNewton approximation plus a quasiNewton approximation to the rest of the Hessian. Even on smallresidual problems, the latter Hessian approximation can be useful when the starting guess is far from the solution. On problems that are not overparameterized (i.e., that do not involve more optimization variables than the data support), NL2SOL usually exhibits fast convergence.
Several internal NL2SOL convergence tolerances are adjusted in response to function_precision
, which gives the relative precision to which responses are computed.
These tolerances may also be specified explicitly using:
convergence_tolerance
(NL2SOL's rfctol
) x_conv_tol
(NL2SOL's xctol
) absolute_conv_tol
(NL2SOL's afctol
) singular_conv_tol
(NL2SOL's sctol
) false_conv_tol
(NL2SOL's xftol
) initial_trust_radius
(NL2SOL's lmax0
)The internal NL2SOL defaults can be obtained for many of these controls by specifying the value 1. The internal defaults are often functions of machine epsilon (as limited by function_precision
).
An example of nl2sol
is given below, and is discussed in the User's Manual.
Note that in this usage of calibration_terms, the driver script rosenbrock
, is returning "residuals", which the nl2sol
method is attempting to minimze. Another use case is to provide a data file, which Dakota will attempt to match the model responses to. See calibration_data_file. Finally, as of Dakota 6.2, the field data capability may be used with nl2sol
. That is, the user can specify field simulation data and field experiment data, and Dakota will interpolate and provide the proper residuals for the calibration.
# Dakota Input File: rosen_opt_nls.in environment tabular_data tabular_data_file = 'rosen_opt_nls.dat' method max_iterations = 100 convergence_tolerance = 1e4 nl2sol model single variables continuous_design = 2 initial_point 1.2 1.0 lower_bounds 2.0 2.0 upper_bounds 2.0 2.0 descriptors 'x1' "x2" interface analysis_driver = 'rosenbrock' direct responses calibration_terms = 2 analytic_gradients no_hessians
NL2SOL has a variety of internal controls as described in AT&T Bell Labs CS TR 153 (http://cm.belllabs.com/cm/cs/cstr/153.ps.gz). A number of existing Dakota controls (method independent controls and responses controls) are mapped into these NL2SOL internal controls. In particular, Dakota's convergence_tolerance
, max_iterations
, max_function_evaluations
, and fd_gradient_step_size
are mapped directly into NL2SOL's rfctol
, mxiter
, mxfcal
, and dltfdj
controls, respectively. In addition, Dakota's fd_hessian_step_size
is mapped into both delta0
and dltfdc
, and Dakota's output
verbosity is mapped into NL2SOL's auxprt
and outlev
(for normal/
prints initial guess, final solution, solution statistics, nondefault values, and changes to the active bound constraint set on every iteration; for verbose/
NL2SOLdebug
output
,quiet
output
, NL2SOL prints only the initial guess and final solution; and for silent
output
, NL2SOL output is suppressed).
These keywords may also be of interest: