Sandia National Laboratories

# convergence_tolerance

Stopping criterion based on objective function or statistics convergence

Topics

method_independent_controls

Specification

- Alias: None

- Arguments: REAL

- Default: 1.e-4

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.

Therefore, permissible values are 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

## Exceptional service in the national interest

© 2023 National Technology and Engineering Solutions of Sandia, LLC. | Questions & Comments | Privacy & Security

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525.