Is abs_() in Gurobi linear or non-linear?

Answered

Muhieddine Shebaro

February 12, 2024 11:13

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I have been trying to model an Mixed Integer Linear Programming problem in Gurobi and I avoided abs_() because I had doubts whether it can make my model non-linear. I researched this online where some say abs_() is non-linear and some others say it does not since Gurobi internally transforms it into a set of linear functions. I already successfully modeled my problem without abs_() just to be in the safe zone, but I just need to know this. Thanks in advance.

Related to

• General Constraints

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 13, 2026 01:30

  This post is more than two 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 try Gurobot, our chatbot interface offering instant, expert-level support.
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  Riley Clement

  • Gurobi Staff

  February 14, 2024 13:04 Edited

  Hi Muhieddine,

  The absolute value function |x| is non-linear, in the general sense.  In Gurobi we linearize this by introducing extra variables and constraints.  If your model was an LP, you can expect (most of the time) that adding an absolute value constraint will make it a MIP.  If you are interested check out the video Advanced Modelling where my colleague Matthias discussed the linearization (around the 20 minute mark).

  - Riley

   

   

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