[Ipopt] IPOpt for l1 optimization?

Peter Carbonetto pcarbo at uchicago.edu
Wed Apr 11 12:33:48 EDT 2012

Is there an absolute value in that objective function you are minimizing? 
If so, then the answer is no, because the objective is non-smooth (it has 
undefined derivatives at zeros). But you can convert this to an equivalent 
smooth optimization problem with additional inequality constraints. There 
is quite a bit of literature on this topic.

Peter Carbonetto, Ph.D.
Postdoctoral Fellow
Dept. of Human Genetics
University of Chicago

On Wed, 11 Apr 2012, Paul van Hoven wrote:

> I've got the following problem:
> min_x sum_{i=1}^N | <x,c_i> |
> s.t. Ax < 0
> <x,c_i> denotes the standard scalar product between x and c_i.
> Is this a problem that can be solved appropriately with IPOpt?
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