Does Model.addGenConstrPWL() (Gurobi 9.0+) use SOS2?

回答済み

Yuhan Tang

2025年12月02日 16:26

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Hello Gurobi Community,

I am writing a model that heavily utilizes piecewise linear constraints using the newer Model.addGenConstrPWL() interface.

I understand from the documentation that:

1. Gurobi versions 9.0 and later provide the specialized addGenConstrPWL() interface.
2. In versions 8.1 and earlier, one had to manually implement these constraints using the Special Ordered Set of Type 2 (SOS2) formulation.

My primary question is regarding the implementation in Gurobi 9.0 and later:

Does the Model.addGenConstrPWL() function internally rely on and automatically generate the standard SOS2 formulation (i.e., the "lambda" formulation with a $\lambda_i \in \text{SOS2}$ constraint)?

Thank you very much!

関連

• Piecewise Linear

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  Maliheh Aramon

  • Gurobi Staff

  2025年12月02日 22:55

  Hi Yuhan, 

  Does the Model.addGenConstrPWL() function internally rely on and automatically generate the standard SOS2 formulation (i.e., the "lambda" formulation with a $\lambda_i \in \text{SOS2}$ constraint)?

  Yes, it does. To approximate the function \(y = f(x)\), the Gurobi Optimizer uses the following set of constraints, where \((x_i, y_i)\) represents the \(i\)-th break point.
  \[ \begin{align} x = \sum_i \lambda_i x_i & \notag \\ y = \sum_i \lambda_i y_i & \notag \\ \sum_i \lambda_i = 1 & \notag \\ \lambda_i \geq 0 ~~\text{and}~~ \text{SOS2} & \notag \end{align} \]

  The first two constraints define the \(x\)- and the \(y\)- coordinates of the piecewise linear function. The third constraint ensures that \((x, y)\) is a convex combination of the breakpoint values. The SOS2 constraint ensures that the only two adjacent \(\lambda_i\) variables can be positive, which enforces that the solution lies on a single segment of the piecewise-linear function. 

  If the function \(f(x)\) is convex, the SOS2 constraints are redundant. 

  Best regards,

  Maliheh
   

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  Yuhan Tang

  2025年12月03日 00:12

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  Thank you so much, Maliheh!

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