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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.<br>
<pre class="moz-signature" cols="72">Andreas Waechter
Associate Professor
Department of Industrial Engineering and Management Sciences
McCormick School of Engineering
Northwestern University
Evanston, IL 60208
USA</pre>
<br>
On 04/11/2012 01:29 PM, Frank E. Curtis wrote:
<blockquote
cite="mid:CAB+Y0=6g2-w==w6eiBXHY9O4VbZF-p2dzTOXNzcgGEcT-cx-0g@mail.gmail.com"
type="cite">
<div>min |x|</div>
<div><br>
</div>
<div>is equivalent to</div>
<div><br>
</div>
<div>min y</div>
<div>s.t. -y <= x <= y, y >= 0</div>
<div><br>
</div>
<div>and equivalent to</div>
<div><br>
</div>
<div>
<div>min y + z</div>
<div>
s.t. x = y - z, (y,z) >= 0</div>
</div>
<div><br>
</div>
<div>The latter two are smooth constrained problems.</div>
<div><br>
</div>
Frank E. Curtis<br>
P. C. Rossin Assistant Professor<br>
Industrial and Systems Engineering<br>
Lehigh University<br>
<a moz-do-not-send="true"
href="http://coral.ie.lehigh.edu/%7Efrankecurtis"
target="_blank">http://coral.ie.lehigh.edu/~frankecurtis</a><br>
<br>
<br>
<div class="gmail_quote">On Wed, Apr 11, 2012 at 2:00 PM, Frank
Kampas <span dir="ltr"><<a moz-do-not-send="true"
href="mailto:fkampas@msn.com">fkampas@msn.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
I think the technique in question is sometimes referred to as
"goal programming".<br>
<br>
-----Original Message----- From: Paul van Hoven<br>
Sent: Wednesday, April 11, 2012 1:51 PM<br>
To: Peter Carbonetto<br>
Cc: <a moz-do-not-send="true"
href="mailto:ipopt@list.coin-or.org" target="_blank">ipopt@list.coin-or.org</a><br>
Subject: Re: [Ipopt] IPOpt for l1 optimization?
<div class="HOEnZb">
<div class="h5"><br>
<br>
Thank you for the answer Peter. Can you recommend some
sources on this<br>
topic of transformation?<br>
<br>
Am 11. April 2012 18:33 schrieb Peter Carbonetto <<a
moz-do-not-send="true" href="mailto:pcarbo@uchicago.edu"
target="_blank">pcarbo@uchicago.edu</a>>:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
Is there an absolute value in that objective function
you are minimizing? If<br>
so, then the answer is no, because the objective is
non-smooth (it has<br>
undefined derivatives at zeros). But you can convert
this to an equivalent<br>
smooth optimization problem with additional inequality
constraints. There is<br>
quite a bit of literature on this topic.<br>
<br>
Peter Carbonetto, Ph.D.<br>
Postdoctoral Fellow<br>
Dept. of Human Genetics<br>
University of Chicago<br>
<br>
<br>
On Wed, 11 Apr 2012, Paul van Hoven wrote:<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
I've got the following problem:<br>
<br>
min_x sum_{i=1}^N | <x,c_i> |<br>
s.t. Ax < 0<br>
<br>
<x,c_i> denotes the standard scalar product
between x and c_i.<br>
<br>
Is this a problem that can be solved appropriately
with IPOpt?<br>
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