L1 norm in objective function

Answered

Paresh Risbud

February 04, 2020 17:00

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Can I include L1 norm in the objective function by using Gurobi 9.0.0? Please let me know.

Thanks,

Paresh

0

• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  June 23, 2025 03:18 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?.
• 

  Yuriy Zinchenko

  • Gurobi Staff

  February 04, 2020 23:37

  Yes, absolutely.  Although we do not have an explicit '\ell-1' construct to accommodate the above norm, we have the absolute value helper function, e.g., 

  https://www.gurobi.com/documentation/9.0/refman/py_abs_.html

  that can be used to get the desired expression. Also note that if you aim to simply minimize the L1 norm expression, you may as well build it yourself as a sequence of convex inequalities that involve auxiliary variables, e.g.,

  min ||x||_1

  is equivalent to

  min t

  s.t.

  x_i <= y_i,

  -x_i <= y_i,

  \sum_i y_i == t

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