SDPA: Leading-edge Software for SDP 2008/10/14 @ Informs ’08 Tokyo Institute of Technology Makoto Yamashita Mituhiro Fukuda Masakazu Kojima Kazuhide Nakata Chuo University Katsuki Fujisawa National Maritime Research Institute Kazuhiro Kobayashi RIKEN Maho Nakata
SDPA: Leading-edge Software for SDP. 2008/10/14 @ Informs ’ 08. SDPA (SemiDefinite Programming Algorithm) Project. Open Source Software to solve SemiDefinite Programming Since the 1 st release in 1995, it has kept high quality - PowerPoint PPT Presentation
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SDPA:Leading-edge Software for SDP
2008/10/14 @ Informs ’08
Tokyo Institute of Technology Makoto YamashitaMituhiro FukudaMasakazu KojimaKazuhide Nakata
Chuo University Katsuki Fujisawa
National Maritime Research Institute Kazuhiro Kobayashi
RIKEN Maho Nakata
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SDPA (SemiDefinite Programming Algorithm) Project
Open Source Software to solveSemiDefinite Programming
Since the 1st release in 1995, it has kept high quality
In 2008, the latest version SDPA 7 was released and has been updated continuously
Many software for more advantage
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SDPA Family
SDPA
SDPARA(Parallel with MPI)
SDPA-C(Matrix Completion)
SDPA-M(Matlab Interface)
SDPA-GMP(Multiple Precision)
SDPARA-C
accessible onSDPA Online Solveras Web service
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Outline of this talk
1. SDP and the improvements of SDPA72. Parallel with MPI3. Multiple Precision4. Online Solver5. Future Works
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Standard form of SDP
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Applications of SDP
Control Theory Lyapnov condition
Combinatorial Optimization Max Cut Theta function
Quantum Chemistry Reduced Density Matrix
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Primal-Dual Interior-Point Methods
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Computation for Search Direction
Schur complement matrix ⇒ Cholesky Factorizaiton
Exploitation of Sparsity in
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SDPA 7
SDPA7 resolves bottlenecks of SDPA6 Introduce sparse Cholesky factorization
for the Schur complement matrix Adopt new data structure Reduce memory space for temporary
variables Introduce configure script for easier
installation
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Sparsity pattern of Schur complement matrix
Fully dense Schur complement matrixFully dense Schur complement matrixSparse Schur complement matrixSparse Schur complement matrixminimum degree ordering minimum degree ordering to minimize to minimize the number of fill-in the number of fill-in
GMP: Gnu Multiple Precision Library Arbitrary fixed precision ‘double’ precision is replaced by GMP Ultra High Accuracy
by long computation time
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Ultra Accuracy of SDPA-GMP
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Comparison on SDPA and SDPA-GMP(384bit)
gpp124-1(SDPLIB)
SDPA-GMP(7.1.0)Relative gap 1.7163710368162993e-26Objective Function -7.3430762652465377e+00 (Primal) -7.3430762652465377e+00 (Dual)Feasibility 2.0710194844721e-57 (Primal) 1.2329417039702e-29 (Dual)Computation time 228.95 sec. (59 iterations)
SDPA(7.1.0)Relative gap 5.3201361904260111e-07Objective Function -7.3430761748645921e+00 (Primal) -7.3430800814821620e+00 (Dual)Feasibility 5.45696821063e-12 (Primal) 1.68252292320e-07 (Dual)Computation time 0.14 sec. (20 iterations)
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SDPA Online Solver
SDPA Online Solver will offer SDPA/SDPARA/SDPARA-C via the Internet.
Internet
InterfaceUser1.Input 2.Ninf-G
3.SDPARA on PC cluster
4.Solution
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To use Online Solver Users without parallel environment can
use SDPARA/SDPARA-C. No Charge. Registration via the Internet is required
so that passwords to protect users data will be generated automatically.
Access SDPA Project Home Page.[SDPA Online for your future.]http://sdpa.indsys.chuo-u.ac.jp/sdpa/
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Online Solver Interface
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Online Solver Usage
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Conclusion The latest version 7 attains higher
performance than version 6 Parallel Solver enables us to solve
extremely large SDPs Matrix Completion is useful for Structural
Sparsity SDPA-GMP generates ultra high accuracy
solution Online Solver provides powerful
computation resources via the Internet
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Future works
Callable Library of SDPA7 Automatic Selection from