convergence_tolerance

Stopping criterion based on objective function or statistics convergence

Topics

method_independent_controls

Specification

  • Alias: None

  • Arguments: REAL

  • Default: 1.e-4

Child Keywords:

Required/Optional

Description of Group

Dakota Keyword

Dakota Keyword Description

Optional (Choose One)

Convergence tolerance type

relative

Assess convergence in adaptive UQ methods using statistical metrics that are relative to a benchmark

absolute

Use absolute statistical metrics for assessing convergence in adaptive UQ methods

Description

The convergence_tolerance specification provides a real value for controlling the termination of iteration.

For optimization, it is most commonly a relative convergence tolerance for the objective function; i.e., if the change in the objective function between successive iterations divided by the previous objective function is less than the amount specified by convergence_tolerance, then this convergence criterion is satisfied on the current iteration.

For uncertainty quantification, it is commonly employed for accuracy control, e.g. in prescribing an upper bound on the variance of a statistical estimator such as the mean value of a QoI. In this context, the tolerance may be either absolute or relative, where the latter admits permissible values between 0 and 1, non-inclusive.

Behavior Varies by Package/Library

This control is used with most optimization and least squares iterators (DOT, CONMIN, NLPQLP, NPSOL, NLSSOL, OPT++, and SCOLIB). Most other Dakota methods (such as DACE or parameter studies) do not use this control, but some adaptive methods, such as adaptive UQ, do.

Since no progress may be made on one iteration followed by significant progress on a subsequent iteration, some libraries require that the convergence tolerance be satisfied on two or more consecutive iterations prior to termination of iteration.

Notes on each library:

  • DOT: relative tolerance that must be satisfied for two consecutive iterations

  • NL2SOL: See nl2sol

  • NLPQLP: used as Lagrangian gradient norm tolerance (ACC), not as a relative convergence tolerance

  • NPSOL: used as a line search tolerance, not as a relative convergence tolerance