# [Ipopt] IPOpt for l1 optimization?

Paul van Hoven paul.van.hoven at googlemail.com
Thu Apr 12 15:12:14 EDT 2012

```Thank you Thomas. I found this here (only for matlab):

http://yall1.blogs.rice.edu/

Am 12. April 2012 16:15 schrieb Thomas Vacek <vacek008 at umn.edu>:
> Perhaps such as http://www.cs.ubc.ca/labs/scl/spgl1/
>
>
>
> On 04/12/2012 02:44 AM, Jonathan Hogg wrote:
>>
>> It may also be worth looking at some of the algorithms used in compressed
>> sensing. I'm told these algorithm don't have any strong complexity results
>> (many are as poor in the worst case), but do exhibit good practical
>> performance on many L1 optimization problems.
>>
>> Jonathan.
>>
>> On 11/04/12 18:51, Paul van Hoven wrote:
>>>
>>> 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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```