<div dir="ltr">Hi Andy,<div><br><div>Interior-point methods give you exactly that: (apart from denegeracy and maybe the presolver) the optimal solution returned by the algorithm is unique and it changes continously with the constraints.</div></div><div><br></div><div>If you also want to include degeneracy, then I have bad news: the optimal solution changes in a non-continous way, and the discontinuities happen when when a constraint is degenerate.</div><div>Imre</div></div><div class="gmail_extra"><br><div class="gmail_quote">On Sun, Mar 1, 2015 at 12:00 PM, <span dir="ltr"><<a href="mailto:clp-request@list.coin-or.org" target="_blank">clp-request@list.coin-or.org</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Send Clp mailing list submissions to<br>
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Today's Topics:<br>
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1. Lexicographic Linear Optimization (Andy Somogyi)<br>
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<br>
Message: 1<br>
Date: Sat, 28 Feb 2015 14:37:00 -0500<br>
From: Andy Somogyi <<a href="mailto:andy.somogyi@gmail.com">andy.somogyi@gmail.com</a>><br>
To: <a href="mailto:clp@list.coin-or.org">clp@list.coin-or.org</a><br>
Subject: [Clp] Lexicographic Linear Optimization<br>
Message-ID: <<a href="mailto:39E324C5-9326-4E97-8590-56E23BC1D165@gmail.com">39E324C5-9326-4E97-8590-56E23BC1D165@gmail.com</a>><br>
Content-Type: text/plain; charset=windows-1252<br>
<br>
Hi All<br>
<br>
Would anyone here have some tips on how to efficiently implement a lexicographic linear optimization in CLP?,<br>
<br>
Basically something similar to the approach outlined in:<br>
<br>
K. H?ffner, S. M. Harwood, and P. I. Barton, ?A reliable simulator for dynamic flux balance analysis,? Biotechnology and bioengineering, vol. 110, no. 3, pp. 792?802, 2013.<br>
<br>
<br>
Currently, I?m doing a pretty cheese approach of performing an iteration over the optimization function coefficients, where I zero all of the coefficients, except for the present one, calculating the primal solution, then set this as a constraint and continue on to the next coefficient, i.e.<br>
<br>
for i,c in orderedObjectives:<br>
zeroModelObjectives();<br>
setModelObjective(i,c);<br>
primal();<br>
setModelConstraint(i, getPrimalSolution(i));<br>
<br>
<br>
Surely this is a very inefficient approach.<br>
<br>
The reason for doing this is that I need a unique solution to the LP problem, and I need that solution to vary continuously in response to smoothly varying constraints.<br>
<br>
Thanks<br>
<br>
? Andy Somogyi, PhD<br>
Research Associate,<br>
Biocomplexity Institute,<br>
Indiana University Dept of Physics<br>
<br>
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End of Clp Digest, Vol 117, Issue 1<br>
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</blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature"><a href="http://imre.polik.net" target="_blank">http://imre.polik.net</a></div>
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