Stopping criterion based on convergence of the objective function

Topics

This keyword is related to the topics:

method_independent_controls

Specification

Alias: none

Argument(s): REAL

Default: 1.e-4

Description

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

It is 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 optimization and least squares iterators (DOT, CONMIN, NPSOL, NLSSOL, OPT++, and SCOLIB) and is not used within the uncertainty quantification, design of experiments, or parameter study iterator branches.

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: must be satisfied for two consecutive iterations
NPSOL: defines an internal optimality tolerance which is used in evaluating if an iterate satisfies the first-order Kuhn-Tucker conditions for a minimum. The magnitude of convergence_tolerance approximately specifies the number of significant digits of accuracy desired in the final objective function (e.g., convergence_tolerance = 1.e-6 will result in approximately six digits of accuracy in the final objective function).
NL2SOL: See nl2sol