# [Ipopt] IPOpt for l1 optimization?

Paul van Hoven paul.van.hoven at googlemail.com
Wed Apr 11 17:41:26 EDT 2012

```Great answer, thank you for your help!

Am 11. April 2012 22:30 schrieb Andreas Waechter <awaechter.iems at gmail.com>:
> And with the linear constraints all together this will be an LP, so you will
> probably be best off with an LP solver rather than a general NLP solver.
>
> Andreas Waechter
>
> Associate Professor
> Department of Industrial Engineering and Management Sciences
> McCormick School of Engineering
> Northwestern University
> Evanston, IL 60208
> USA
>
>
> On 04/11/2012 01:29 PM, Frank E. Curtis wrote:
>
> min |x|
>
> is equivalent to
>
> min y
> s.t. -y <= x <= y, y >= 0
>
> and equivalent to
>
> min y + z
> s.t. x = y - z, (y,z) >= 0
>
> The latter two are smooth constrained problems.
>
> Frank E. Curtis
> P. C. Rossin Assistant Professor
> Industrial and Systems Engineering
> Lehigh University
> http://coral.ie.lehigh.edu/~frankecurtis
>
>
> On Wed, Apr 11, 2012 at 2:00 PM, Frank Kampas <fkampas at msn.com> wrote:
>>
>> 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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>
>
>
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```