Dakota Reference Manual  Version 6.12
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linear_equality_constraint_matrix


Define coefficients of the linear equalities

Topics

This keyword is related to the topics:

Specification

Alias: none

Argument(s): REALLIST

Default: no linear equality constraints

Description

In the equality case, the constraint matrix $A$ provides coefficients for the variables on the left hand side of:

\[Ax = a_t\]

The linear_constraints topics page (linked above) outlines a few additional things to consider when using linear constraints.

Examples

An optimization involving three variables, x1, x2, and x3, is to be performed. These variables must satisfy a pair of linear equality constraints:

\[ 1.5 \cdot x1 + 1.0 \cdot x2 = 5.0 \]

\[ 3.0 \cdot x1 - 4.0 \cdot x3 = 0.0 \]

The pair of constraints can be written in matrix form as:

\[\begin{bmatrix} 1.5 & 1.0 & 0.0 \\ 3.0 & 0.0 & -4.0 \end{bmatrix} \begin{bmatrix} x1 \\ x2 \\ x3 \end{bmatrix} = \begin{bmatrix} 5.0 \\ 0.0 \end{bmatrix} \]

The coefficient matrix and right hand side are expressed to Dakota in the variables section of the input file:

variables
  continuous_design 2
    descriptors 'x1' 'x2'

  linear_equality_constraint_matrix = 1.5  1.0  0.0
                                      3.0  0.0 -4.0

  linear_equality_targets = 5.0
                            0.0

For related examples, see the linear_inequality_constraint_matrix keyword page.