[Ipopt] IPOpt for l1 optimization?

[Frank Kampas]

I think the technique in question is sometimes referred to as "goal 
programming".

-----Original Message----- 
From: Paul van Hoven
Sent: Wednesday, April 11, 2012 1:51 PM
To: Peter Carbonetto
Cc: ipopt at list.coin-or.org
Subject: Re: [Ipopt] IPOpt for l1 optimization?

Thank you for the answer Peter. Can you recommend some sources on this
topic of transformation?

Am 11. April 2012 18:33 schrieb Peter Carbonetto <pcarbo at uchicago.edu>:
> 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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>
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