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