1Blurb::
2Define coefficients of the linear equalities
3Description::
4In the equality case, the constraint matrix \f$A\f$
5provides coefficients for the variables on the left hand side of:
6\f[Ax = a_t\f]
7
8The linear_constraints topics page (linked above) outlines a few additional
9things to consider when using linear constraints.
10
11Topics::	linear_constraints
12Examples::
13An optimization involving three variables, \c x1, \c x2, and \c x3, is to be
14performed. These variables must satisfy a pair of linear equality constraints:
15
16\f[ 1.5 \cdot x1 + 1.0 \cdot x2 = 5.0 \f]
17\f[ 3.0 \cdot x1 - 4.0 \cdot x3 = 0.0 \f]
18
19The pair of constraints can be written in matrix form as:
20
21\f[\begin{bmatrix}
22  1.5 & 1.0 & 0.0 \\
23  3.0 & 0.0 & -4.0
24\end{bmatrix}
25
26\begin{bmatrix}
27  x1 \\
28  x2 \\
29  x3
30\end{bmatrix}
31=
32\begin{bmatrix}
33  5.0 \\
34  0.0
35\end{bmatrix}
36
37\f]
38
39The coefficient matrix and right hand side are expressed to Dakota in the
40\ref variables section of the input file:
41
42\verbatim
43
44variables
45  continuous_design 2
46    descriptors 'x1' 'x2'
47
48  linear_equality_constraint_matrix = 1.5  1.0  0.0
49                                      3.0  0.0 -4.0
50
51  linear_equality_targets = 5.0
52                            0.0
53
54\endverbatim
55
56For related examples, see the \ref variables-linear_inequality_constraint_matrix
57keyword page.
58
59Theory::
60Faq::
61See_Also::
62