<div dir="ltr"><div>Dear Julian, </div><div><br></div><div>In O(m^2), m is max (row, column) ? </div><div><br></div><div>Thanks</div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div class="gmail_extra"><br><div class="gmail_quote">On Mon, May 9, 2016 at 5:40 PM, OR MSc <span dir="ltr"><<a href="mailto:ormsc@ed.ac.uk" target="_blank">ormsc@ed.ac.uk</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;padding-left:1ex;border-left-color:rgb(204,204,204);border-left-width:1px;border-left-style:solid">Dear Usa<span><br>
<br>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;padding-left:1ex;border-left-color:rgb(204,204,204);border-left-width:1px;border-left-style:solid">
What if I find a machine with memory large enough to hold the matrix ?<br>
<br>
Are there some internal limits about the matrix size inside CLP<br>
implementation ?<br>
</blockquote>
<br></span>
The only limit I can think could be reached occurs when the number of nonzeros reaches what can be stored in a 4-byte integer<span><br>
<br>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;padding-left:1ex;border-left-color:rgb(204,204,204);border-left-width:1px;border-left-style:solid">
Especially, the limits about matrix inversion or other matrix operations ?<br>
</blockquote>
<br></span>
No: so long as there is enough memory, Clp will allocate O(m^2) memory to store the LU factors of the basis.<br>
<br>
Marginally, the number of updates which the simplex method will perform may be limited by the available memory, increasing the frequency with which refactorization takes place but decreasing the iteration speed.<br>
<br>
With a very dense problem the sparsity-exploiting numerical linear algebra may be<br>
<br>
Of course, I didn't write Clp, but I've written a comparable system so know of the issues involved.<br>
<br>
Julian<br>
<br>
PS Sorry if you've already received this reply!<br>
<br>
<br>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;padding-left:1ex;border-left-color:rgb(204,204,204);border-left-width:1px;border-left-style:solid"><span>
On Mon, May 9, 2016 at 4:51 AM, Julian Hall <<a href="mailto:jajhall@ed.ac.uk" target="_blank">jajhall@ed.ac.uk</a><br></span><span>
<mailto:<a href="mailto:jajhall@ed.ac.uk" target="_blank">jajhall@ed.ac.uk</a>>> wrote:<br>
<br>
Dear Usa<br>
<br>
Not a hope. With no sparsity to exploit, your problem has 3.5G<br>
values, each needing 8B of memory. To solve the problem with Clp<br>
probably needs about 80G memory.<br>
<br>
Both your problem dimensions are at least half an order of magnitude<br>
too large.<br>
<br>
Julian<br>
<br>
<br>
On 9 May 2016 04:56:45 BST, usa usa <<a href="mailto:usact2012@gmail.com" target="_blank">usact2012@gmail.com</a><br></span><span>
<mailto:<a href="mailto:usact2012@gmail.com" target="_blank">usact2012@gmail.com</a>>> wrote:<br>
<br>
Hi,<br>
<br>
I would like to solve a linear programming model by CLP on a<br>
laptop with 8 GB memory.<br>
<br>
It has 35,000 dec. variables and 100,000 constraints.<br>
<br>
The constraint matrix is very dense.<br>
<br>
Is it possible to solve this size of LP model by CLP ?<br>
<br>
Any advices would be appreciated.<br>
<br>
thanks !<br>
<br></span>
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</span></blockquote><span><font color="#888888">
<br>
-- <br>
Julian Hall (Postgraduate Taught Programme Coordinator - Operational Research MSc Programme Director)<br>
--<br>
Dr. J. A. Julian Hall, Senior Lecturer, School of Mathematics,<br>
University of Edinburgh, James Clerk Maxwell Building,<br>
Peter Guthrie Tait Road, EDINBURGH, EH9 3FD, UK.<br>
Room: 6221 Phone: [+44](131) 650 5075 Email: <a href="mailto:J.A.J.Hall@ed.ac.uk" target="_blank">J.A.J.Hall@ed.ac.uk</a><br>
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<br>
The University of Edinburgh is a charitable body, registered in<br>
Scotland, with registration number SC005336.<br>
<br>
</div></div></blockquote></div><br></div></div>