Dakota Reference Manual  Version 6.2
Large-Scale Engineering Optimization and Uncertainty Analysis
 All Pages

Trust-region 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 X-convergence 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 model_pointer

Identifier for model block to be used by a method


NL2SOL is available as nl2sol and addresses unconstrained and bound-constrained least squares problems. It uses a trust-region method (and thus can be viewed as a generalization of the Levenberg-Marquardt algorithm) and adaptively chooses between two Hessian approximations, the Gauss-Newton approximation alone and the Gauss-Newton approximation plus a quasi-Newton approximation to the rest of the Hessian. Even on small-residual problems, the latter Hessian approximation can be useful when the starting guess is far from the solution. On problems that are not over-parameterized (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
    tabular_data_file = 'rosen_opt_nls.dat'

  max_iterations = 100
  convergence_tolerance = 1e-4


  continuous_design = 2
    initial_point    -1.2      1.0
    lower_bounds     -2.0     -2.0
    upper_bounds      2.0      2.0
    descriptors       'x1'     "x2"

  analysis_driver = 'rosenbrock'

  calibration_terms = 2


NL2SOL has a variety of internal controls as described in AT&T Bell Labs CS TR 153 (http://cm.bell-labs.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/verbose/debug output, NL2SOL prints initial guess, final solution, solution statistics, nondefault values, and changes to the active bound constraint set on every iteration; for quiet output, NL2SOL prints only the initial guess and final solution; and for silent output, NL2SOL output is suppressed).

See Also

These keywords may also be of interest: