lumix.nonlinear.terms.LXBilinearTerm

class lumix.nonlinear.terms.LXBilinearTerm(var1, var2, coefficient=1.0)[source]

Product of two variables: x * y.

Represents the product of two decision variables, which is nonlinear but can be linearized using different techniques depending on the variable types.

The linearization method is automatically selected based on variable types:

  • Binary × Binary: AND logic (z <= x, z <= y, z >= x+y-1)

  • Binary × Continuous: Big-M method

  • Continuous × Continuous: McCormick envelopes (requires bounds)

Parameters:
var1

First variable in the product.

var2

Second variable in the product.

coefficient

Coefficient to multiply the product by (default: 1.0).

Example

Facility activation times flow:

from lumix.nonlinear import LXBilinearTerm
from lumix.core import LXVariable

# Flow is only active if facility is open
is_open = LXVariable[Facility, int]("is_open").binary()
flow_amount = LXVariable[Facility, float]("flow").continuous()

# actual_flow = is_open * flow_amount
actual_flow = LXBilinearTerm(
    var1=is_open,
    var2=flow_amount,
    coefficient=1.0
)

Rectangle area calculation:

# Area = length * width (both continuous)
length = LXVariable[Shape, float]("length").continuous().bounds(1, 10)
width = LXVariable[Shape, float]("width").continuous().bounds(1, 10)

area = LXBilinearTerm(var1=length, var2=width)

Weighted product:

# Price * quantity with discount factor
revenue = LXBilinearTerm(
    var1=price,
    var2=quantity,
    coefficient=0.9  # 10% discount
)

Note

For Continuous × Continuous products, both variables MUST have finite bounds defined. McCormick envelopes require knowing the variable bounds to construct the linearization.

The linearization introduces auxiliary variables and constraints that ensure the auxiliary variable equals the product of the two input variables.

__init__(var1, var2, coefficient=1.0)
Parameters:
Return type:

None

Methods

__init__(var1, var2[, coefficient])

Attributes

coefficient

var1

var2

var1: LXVariable
var2: LXVariable
coefficient: float = 1.0
__init__(var1, var2, coefficient=1.0)
Parameters:
Return type:

None