lumix.nonlinear.terms.LXMinMaxTerm

class lumix.nonlinear.terms.LXMinMaxTerm(vars, operation, coefficients)[source]

Min/Max of multiple variables.

Represents the minimum or maximum value among a set of variables. This is linearized by introducing an auxiliary variable z and adding constraints that ensure z equals the min or max of the input variables.

Parameters:
vars

List of variables to take min/max over.

operation

Either “min” or “max” to specify the operation.

coefficients

Coefficients for each variable in the min/max operation.

Example

Minimum cost selection:

from lumix.nonlinear import LXMinMaxTerm
from lumix.core import LXVariable

# Select minimum cost among alternatives
cost_a = LXVariable[Option, float]("cost_a").from_data(options_a)
cost_b = LXVariable[Option, float]("cost_b").from_data(options_b)
cost_c = LXVariable[Option, float]("cost_c").from_data(options_c)

min_cost = LXMinMaxTerm(
    vars=[cost_a, cost_b, cost_c],
    operation="min",
    coefficients=[1.0, 1.0, 1.0]
)

Maximum capacity:

# Find maximum capacity among resources
max_capacity = LXMinMaxTerm(
    vars=[cap_1, cap_2],
    operation="max",
    coefficients=[1.0, 1.0]
)

Note

Linearization for min: Introduces auxiliary variable z with constraints z <= x_i for all i. For max: z >= x_i for all i.

The auxiliary variable z represents the result of the min/max operation and can be used in subsequent constraints or the objective function.

__init__(vars, operation, coefficients)
Parameters:
Return type:

None

Methods

__init__(vars, operation, coefficients)

Attributes

vars

operation

coefficients

vars: List[LXVariable]
operation: Literal['min', 'max']
coefficients: List[float]
__init__(vars, operation, coefficients)
Parameters:
Return type:

None