A parallel primal-dual interior-point method for semidefinite programs using positive definite matrix completion

Parallel Computing

Volumn 32, Issue 1, 2006, Pages 24-43

  Nakata, Kazuhide ^a   Yamashita, Makoto ^b   Fujisawa, Katsuki ^c   Kojima, Masakazu ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b KANAGAWA UNIVERSITY   (Japan)

^c TOKYO DENKI UNIVERSITY   (Japan)

Author keywords

Numerical experiment; Parallel computation; PC cluster; Positive definite matrix completion; Primal dual interior point method; Semidefinite program

Indexed keywords

MATRIX ALGEBRA; PARALLEL PROCESSING SYSTEMS; PERSONAL COMPUTERS; PROBLEM SOLVING;

PC CLUSTER; POSITIVE DEFINITE MATRIX COMPLETION; PRIMAL-DUAL INTERIOR-POINT METHOD; SEMIDEFINITE PROGRAM;

COMPUTER SOFTWARE;

EID: 29244441161     PISSN: 01678191     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.parco.2005.07.002     Document Type: Article

References (29)

1. S.J. Benson, Parallel computing on semidefinite programs, Preprint ANL/MCS-P939-0302, Available from: < http://www.msc.anl.gov/~benson/dsdp/ pdsdp.ps > (2002).
2. S.J. Benson, Y. Ye, and X. Zhang Solving large-scale sparse semidefinite programs for combinatorial optimization SIAM Journal on Optimization 10 2000 443 461
3. A. Ben-Tal, M. Kocvara, A. Nemirovskii, and J. Zowe Free material optimization via semidefinite programming: the multiload case with contact conditions SIAM Journal on Optimization 9 1999 813 832
4. A. Ben-Tal, and A. Nemirovskii Lectures on Modern Convex Optimization Analysis, Algorithms, and Engineering Applications 2001 SIAM Philadelphia
5. L.S. Blackford, J. Choi, A. Cleary, E. D'Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, and R.C. Whaley ScaLAPACK Users' Guide 1997 SIAM Philadelphia
6. B. Borchers CSDP 2.3 user's guide Optimization Methods and Software 11&12 1999 597 611 Available from: < http://www.nmt.edu/~borchers/csdp. html
7. B. Borchers SDPLIB 1.2, a library of semidefinite programming test problems Optimization Methods and Software 11&12 1999 683 690
8. S. Burer Semidefinite programming in the space of partial positive semidefinite matrices SIAM Journal on Optimization 14 2003 139 172
9. S. Burer, R.D.C. Monteiro, and Y. Zhang A computational study of a gradient-based log-barrier algorithm for a class of large-scale SDPs Mathematical Programming 95 2003 359 379
10. C. Choi, Y. Ye, Solving sparse semidefinite programs using the dual scaling algorithm with an iterative solver, Manuscript, Department of Management Sciences, University of Iowa, Iowa City, IA 52242, 2000.
11. K. Fujisawa, M. Kojima, and K. Nakata Exploiting sparsity in primal-dual interior-point methods for semidefinite programming Mathematical Programming 79 1997 235 253
12. M. Fukuda, M. Kojima, K. Murota, and K. Nakata Exploiting sparsity in semidefinite programming via matrix completion. I: General framework SIAM Journal on Optimization 11 2000 647 674
13. D.R. Fulkerson, and J.W.H. Gross Incidence matrices and interval graphs Pacific Journal of Mathematics 15 1965 835 855
14. D. Goldfarb, and G. Iyengar Robust portfolio selection problems Mathematics of Operations Research 28 2003 1 38
15. W. Gropp, E. Lusk, and A. Skjellum Using MPI: Portable Parallel Programming with the Message-Passing Interface 1994 MIT Press Massachusetts
16. C. Helmberg, and F. Rendl A spectral bundle method for semidefinite programming SIAM Journal on Optimization 10 2000 673 696
17. M. Kocvara, and M. Stingl PENNON-a code for convex nonlinear and semidefinite programming Optimization Methods and Software 18 2003 317 333
18. M. Kojima, S. Shindoh, and S. Hara Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices SIAM Journal on Optimization 7 1997 86 125
19. R.D.C. Monteiro First- and second-order methods for semidefinite programming Mathematical Programming 97 2003 209 244
20. K. Nakata, K. Fujisawa, M. Fukuda, M. Kojima, and K. Murota Exploiting sparsity in semidefinite programming via matrix completion. II: Implementation and numerical results Mathematical Programming 95 2003 303 327
21. K. Nakata, K. Fujisawa, and M. Kojima Using the conjugate gradient method in interior-point methods for semidefinite programs (in Japanese) Proceedings of the Institute of Statistical Mathematics 46 1998 297 316
22. M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, and K. Fujisawa Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm Journal of Chemical Physics 114 2001 8282 8292
23. J.F. Sturm Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones Optimization Methods and Software 11&12 1999 625 653
24. K.C. Toh, and M. Kojima Solving some large scale semidefinite programs via conjugate residual method SIAM Journal on Optimization 12 2002 669 691
25. K.C. Toh, M.J. Todd, and R.H. Tütüncü SDPT3-a MATLAB software package for semidefinite programming, version 1.3 Optimization Methods and Software 11&12 1999 545 581 Available from: < http://www.math.nus. edu.sg/~mattohkc >
26. H. Waki, S. Kim, M. Kojima, M. Muramatsu, Sums of squares and semidefinite programming relaxations for polynomial optimization problems with structured sparsity, Research Report B-411, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo 152-8552, 2005.
27. H. Wolkowicz R. Saigal L. Vandenberghe Handbook of Semidefinite Programming, Theory, Algorithms, and Applications 2000 Kluwer Academic Publishers Massachusetts
28. M. Yamashita, K. Fujisawa, and M. Kojima Implementation and Evaluation of SDPA 6.0 (SemiDefinite Programming Algorithm 6.0) Optimization Methods and Software 18 2003 491 505
29. M. Yamashita, K. Fujisawa, and M. Kojima SDPARA: semidefinite programming algorithm parallel version Parallel Computing 29 2003 1053 1067