1 norm or absolute value in JuMP?

[Sarah Koehler]

Hello,

I am trying to use a Tikhonov regularization in JuMP but it seems I cannot get it to work. I have tried abs(), norm() in combination with sum{...} and I usually get something like: 

"Unrecognized function abs"

I even tried @setNLObjective and that seems to give me the same error. Is this not supported or am I missing something obvious? Thanks!

-Sarah

[Miles Lubin]

Hi Sarah,

If you're using a convex l1 regularization term, the best approach is to add a few auxiliary variables and linear inequality constraints as follows:

# to represent |x|

@defVar(m, z)

@addConstraint(m, z >= x)

@addConstraint(m, z >= -x)

Systems like CVX and Convex.jl do this transformation automatically, after verifying that the problem is indeed convex (this transformation is not valid otherwise). In JuMP, you currently have to do this transformation by hand.

Miles

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[Sarah Koehler]

Okay so I just have to use a slack variable. Alright, thanks!

[Iain Dunning]

Norms are on our mind though, so keep a look out.

Btw, is your objective linear/quadratic? I noticed you were using @setNLObjective.

--

Iain Dunning

PhD Candidate / MIT Operations Research Center

http://iaindunning.com  /  http://juliaopt.org

[Sarah Koehler]

Oh no, my objective is convex quadratic. I just tried @setNLObjective in case support for the 1 norm had somehow slipped under the radar for the regular @setObjective.