[Ipopt] IPOpt for l1 optimization?

[Thomas Vacek]

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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>