Dakota Reference Manual: lagrangian_objective

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lagrangian_objective

Lagrangian approximate subproblem formulation

## Specification

Alias: none

Argument(s): none

## Description

For SBL problems with nonlinear constraints, a number of algorithm formulations exist as described in[21] and as summarized in the Advanced Examples section of the Models chapter of the Users Manual[4]. First, the "primary" functions (that is, the objective functions or calibration terms) in the approximate subproblem can be selected to be surrogates of the original primary functions (`original_primary`), a single objective function (`single_objective`) formed from the primary function surrogates, or either an augmented Lagrangian merit function (`augmented_lagrangian_objective`) or a Lagrangian merit function (`lagrangian_objective`) formed from the primary and secondary function surrogates. The former option may imply the use of a nonlinear least squares method, a multiobjective optimization method, or a single objective optimization method to solve the approximate subproblem, depending on the definition of the primary functions. The latter three options all imply the use of a single objective optimization method regardless of primary function definition.