Adding constraints to the model
The next step in the example is to add our two linear constraints.
This is done by building a sparse matrix that captures the constraint
# Build (sparse) constraint matrix data = np.array([1.0, 2.0, 3.0, -1.0, -1.0]) row = np.array([0, 0, 0, 1, 1]) col = np.array([0, 1, 2, 0, 1]) A = sp.csr_matrix((data, (row, col)), shape=(2, 3))
The matrix has two rows, one for each constraint, and three columns,
one for each variable in our matrix variable.
col arrays gives the row and column indices
for the 5 non-zero values in the sparse matrix, respectively. The
val array gives the numerical values.
Note that we multiply
the greater-than constraint by to transform it to a less-than
We also capture the right-hand side in a NumPy array:
# Build rhs vector rhs = np.array([4.0, -1.0])
We then use the overloaded
@ operator to build a linear matrix
expression, and then use the overloaded less-than-or-equal operator to
add two constraints (one for each row in the matrix expression):
# Add constraints m.addConstr(A @ x <= rhs, name="c")