# dimod.binary.BinaryQuadraticModel.add_linear_equality_constraint¶

BinaryQuadraticModel.add_linear_equality_constraint(terms: , lagrange_multiplier: , constant: )[source]

Add a linear constraint as a quadratic objective.

Adds a linear constraint of the form $$\sum_{i} a_{i} x_{i} + C = 0$$ to the binary quadratic model as a quadratic objective.

Parameters
• terms – Values of the $$\sum_{i} a_{i} x_{i}$$ term as an $$i$$–length iterable of 2-tuples, (variable, bias), with each tuple constituting a term in the summation.

• lagrange_multiplier – Weight or penalty strength. The linear constraint is multiplied by this value (which does not appear explicitly in the above equation) when added to the binary quadratic model.

• constant – Value of the constant term, $$C$$, of the linear constraint.

Examples

>>> bqm = dimod.BinaryQuadraticModel("BINARY")
>>> bqm.add_linear_equality_constraint([("x1", 5), ("x2", -2)], 10, -3)
>>> print(bqm)
BinaryQuadraticModel({'x1': -50.0, 'x2': 160.0}, {('x2', 'x1'): -200.0}, 90.0, 'BINARY')