linear_equality_constraint_matrix

Define coefficients of the linear equalities

Topics

linear_constraints

Specification

• Alias: None

• Arguments: 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:

$$\begin{array}{r}\left[\begin{array}{ccc}1.5& 1.0& 0.0\\ 3.0& 0.0& -4.0\end{array}\right]\left[\begin{array}{c}x1\\ x2\\ x3\end{array}\right]=\left[\begin{array}{c}5.0\\ 0.0\end{array}\right]\end{array}$$

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.