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I was trying to use Gurobi for a minimization problem like so: $$ \min\|M-TX\|_1 $$ where all three terms are matrices. $X$ is the nonnegative decision variable(s) of compatible size. $M$ and $T$ are nonnegative. I wanted $TX$ to approximate $M$, with $X$ being as sparse as possible in an LP. I also have some other constraints on $X$.

It seems that the MVar support in Gurobi v10 doesn't yet have a norm function, and that its general norm function only supports vectors, and that its reshape support only applies to variables, not to expressions. How can I achieve my objective?

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Brannon
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    Are you open to linearization? – RobPratt Jan 02 '23 at 17:36
  • @RobPratt, I think so. Some of my constraints on $X$ take advantage of its matrix form, but they can be adjusted. – Brannon Jan 02 '23 at 17:43
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    You want to minimize a sum of absolute values of a linear function of $X$. See https://or.stackexchange.com/questions/114/how-to-minimize-an-absolute-value-in-the-objective-of-an-lp – RobPratt Jan 02 '23 at 17:45

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