Blurb::
Define coefficients of the linear equalities
Description::
In the equality case, the constraint matrix \f$A\f$
provides coefficients for the variables on the left hand side of:
\f[Ax = a_t\f]

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

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

\f[ 1.5 \cdot x1 + 1.0 \cdot x2 = 5.0 \f]
\f[ 3.0 \cdot x1 - 4.0 \cdot x3 = 0.0 \f]

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

\f[\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}

\f]

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

\verbatim

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

\endverbatim

For related examples, see the \ref variables-linear_inequality_constraint_matrix
keyword page.

Theory::
Faq::
See_Also::	
