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http:^^www.cs.cornell.edu^info^people^mwagner^ppcx^ppcx2.html

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<!DOCTYPE HTML PUBLIC -//AS//DTD HTML 3.0 asWedit + extensions//EN><HTML><HEAD><TITLE> pPCx </title></HEAD><BODY bgcolor="#ffffff" link="#ff0000" vlink="#426F42" alink="#ffffff"><!BODY background="back.jpg" link="#ff0000" vlink="#426F42"alink="#ffffff"><H1 align=center>The pPCx page</H1><P>pPCx stands for "parallel predictor corrector" package and is aparallel version of the PCx code for Linear Programming developed atthe <!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><A HREF="http://www.mcs.anl.gov/home/otc/">Optimization TechnologyCenter</A> at <!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><A HREF="http://www.mcs.anl.gov/">Argonne NationalLabs</A>. This is work in progress, people involved from the Cornellside are <!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><AHREF="http://www.cs.cornell.edu/Info/People/coleman/coleman.html">Thomas Coleman</A>, <!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><A HREF="http://www.cs.cornell.edu/Info/People/csun/sun.html">Chunguang Sun</A> and <!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><A HREF="http://www.orie.cornell.edu">Michael Wagner</A>,and <!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><A HREF="http://www.mcs.anl.gov/home/wright/">Steve Wright</A>from Argonne. <P>The basic framework for pPCx is <!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><A HREF="http://www.iems.nwu.edu/faculty/mehrotra.html">Mehrotra</A>'spredictor corrector interior point method for linear programming. Most of thework in an interior point method lies in solving a symmetric sparsepositive (semi-) definite system of linearequations: we use a new <!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><A HREF="http://www.cs.cornell.edu/Info/People/csun/psspd/index.html">parallel multifrontal Cholesky factorization</A>developed by <!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><A HREF="http://www.cs.cornell.edu/Info/People/csun/sun.html">Chunguang Sun</A> that efficiently handles near-degeneracies. We alsotake care of dense rows and columns efficiently so that we can exploitsparsity in the normal equations as much as possible.The constraint matrix is stored in a distributed form, thus enabling thesolution of very large problems that cannot be solved on a singleprocessor.</P>The code is written entirely in C (with MPI extensions) andwill thus be easily portable to other architectures.The testing is being done in the <!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><A HREF="http://www.tc.cornell.edu/Research/ACRI/">ACRI</A> on the IBM SP2 at the <!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><A HREF="http://www.tc.cornell.edu">Cornell Theory Center</A><P>Here are a few of the papers that are relevant for the development ofthis code:<UL><LI>S. J. Wright, <!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><A HREF="http://www.mcs.anl.gov/home/wright/papers/P600.ps">"Modified Cholesky Factorizations in Interior-Point Algorithms for LinearProgramming,"</A>Preprint ANL/MCS-P600-0596, May, 1996.<LI>S. Mehrotra, "On the implementation of a primal-dual interiorpoint method", SIAM Journal on Optimization, 2 (1992), pp. 575-601</UL>For other interior page pages check out <!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><AHREF="http://www.mcs.anl.gov/home/otc/InteriorPoint/">Interior Points Online</A>.<P>Back to the <!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><A HREF="http://www.cs.cornell.edu/Info/Projects/ccop">CCOP-homepage</A>....<P> <HR> <ADDRESS> Please send comments or suggestions to<!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><A HREF=mailto:"mwagner@cs.cornell.edu">mwagner@cs.cornell.edu</A><BR></ADDRESS><HR></BODY>Last update: Fri Oct 25 12:23:20 EDT 1996</HTML>

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