# LinearExpression¶

Significant speed improvements can be obtained using the LinearExpression object when there are long, dense, linear expressions. The arguments are

constant, linear_coeffs, linear_vars


where the second and third arguments are lists that must be of the same length. Here is a simple example that illustrates the syntax. This example creates two constraints that are the same:

>>> import pyomo.environ as pyo
>>> from pyomo.core.expr.numeric_expr import LinearExpression
>>> model = pyo.ConcreteModel()
>>> model.nVars = pyo.Param(initialize=4)
>>> model.N = pyo.RangeSet(model.nVars)
>>> model.x = pyo.Var(model.N, within=pyo.Binary)
>>>
>>> model.coefs = [1, 1, 3, 4]
>>>
>>> model.linexp = LinearExpression(constant=0,
...                                 linear_coefs=model.coefs,
...                                 linear_vars=[model.x[i] for i in model.N])
>>> def caprule(m):
...     return m.linexp <= 6
>>> model.capme = pyo.Constraint(rule=caprule)
>>>
>>> def caprule2(m):
...     return sum(model.coefs[i-1]*model.x[i] for i in model.N) <= 6
>>> model.capme2 = pyo.Constraint(rule=caprule2)


Warning

The lists that are passed to LinearModel are not copied, so caution must be excercised if they are modified after the component is constructed.