How to define a semi-continuous variable in Gurobi/Python?

Answered

Amin Shahmardan

August 19, 2021 17:38

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Hi

Suppose we have a continuous variable "x" and a parameter "\theta". Now, we want to define the variable "y" as follows:

y = \theta*x   if x>0; 

      0             if x=0

I would be thankful to know how to model y. Thanks

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  June 23, 2025 02:49 Edited

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum. Or why not try our AI Gurobot?.
• 

  Eli Towle

  • Gurobi Staff

  August 19, 2021 21:02

  You can model this relationship with the single constraint \( y = \theta x \). If \( x \) equals \( 0 \), then \( \theta x \) also equals \( 0 \).

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