L1 norm in objective function

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Paresh Risbud

• February 04, 2020 17:00

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

Thanks,

Paresh

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  Yuriy Zinchenko

  • 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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