# Model.addConstrs()

###

Model.addConstrs()

addConstrs ( generator, name="" )
Add multiple constraints to a model using a Python generator expression. Returns a Gurobi tupledict that contains the newly created constraints, indexed by the values generated by the generator expression.

The first argument to `addConstrs`

is a Python generator
expression, a special feature of the Python language that allows you
to iterate over a Python expression. In this case, the Python
expression will be a Gurobi constraint and the generator expression
provides values to plug into that constraint. A new Gurobi constraint
is added to the model for each iteration of the generator expression.

To give an example, if `x`

is a Gurobi variable, then

m.addConstr(x <= 1, name='c0')would add a single linear constraint involving this variable. In contrast, if

`x`

is a list of Gurobi variables, then
m.addConstrs((x[i] <= 1 for i in range(4)), name='c')would add four constraints to the model. The entire first argument is a generator expression, where the indexing is controlled by the statement

`for i in range(4)`

, The first constraint that results
from this expression would be named `c[0]`

, and would involve
variable `x[0]`

. The second would be named `c[1]`

, and
would involve variable `x[1]`

.
Generator expressions can be much more complex than this. They can involve multiple variables and conditional tests. For example, you could do:

m.addConstrs((x[i,j] == 0 for i in range(4) for j in range(4) if i != j), name='c')

One restriction that `addConstrs`

places on the generator
expression is that each variable must always take a scalar value
(`int`

, `float`

, `string`

, ...). Thus,
`for i in [1, 2.0, 'a', 'bc']`

is fine, but
`for i in [(1, 2), [1, 2, 3]]`

isn't.

This method can be used to add linear constraints, quadratic constraints, or general constraints to the model. Refer to the TempConstr documentation for more information on all of the different constraint types that can be added.

Note that if you supply a name argument, the generator expression must be enclosed in parenthesis. This requirement comes from the Python language interpreter.

Arguments:

generator: A generator expression, where each iteration produces a constraint.

name: Name pattern for new constraints. The given name will be subscripted by the index of the generator expression, so if the index is an integer, c would become c[0], c[1], etc. Note that the generated names will be stored as ASCII strings, so you should avoid using names that contain non-ASCII characters. In addition, names that contain spaces are strongly discouraged, because they can't be written to LP format files.

Return value:

A dictionary of Constr objects, indexed by the values specified by the generator expression.

**Example usage:**

model.addConstrs(x.sum(i, '*') <= capacity[i] for i in range(5)) model.addConstrs(x[i] + x[j] <= 1 for i in range(5) for j in range(5)) model.addConstrs(x[i]*x[i] + y[i]*y[i] <= 1 for i in range(5)) model.addConstrs(x.sum(i, '*') == [0, 2] for i in [1, 2, 4]) model.addConstrs(z[i] == max_(x[i], y[i]) for i in range(5)) model.addConstrs((x[i] == 1) >> (y[i] + z[i] <= 5) for i in range(5))

**Warning**- A constraint can only have a single comparison operator.

While`1 <= x + y <= 2`or`1 <= x[i] + y[i] <= 2 for i in range(3)`

may look like valid constraints, our Python API won't interpret them as they were intended, which will almost

certainly result in unexpected behavior.