1 comment

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