Implementation of a primal-dual method for SDP on a shared memory parallel architecture

Computational Optimization and Applications

Volumn 37, Issue 3, 2007, Pages 355-369

  Borchers, Brian ^a   Young, Joseph G ^b  

^a NEW MEXICO INSTITUTE OF MINING AND TECHNOLOGY   (United States)

^b Rice University   (United States)

Author keywords

Interior point methods; Parallel computing; Semidefinite programming

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER ARCHITECTURE; COMPUTER SOFTWARE; PROBLEM SOLVING; STORAGE ALLOCATION (COMPUTER);

INTERIOR POINT METHODS; SEMIDEFINITE PROGRAMMING;

PARALLEL PROCESSING SYSTEMS;

EID: 34547344235     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-007-9030-3     Document Type: Article

References (21)

1. Anderson, E., Bai, Z., Bischof, C., Blackford, L.S., Demmel, J., Dongarra, J.J., Du Croz, J., Hammarling, S., Greenbaum, A., McKenney, A., Sorensen, D.: LAPACK Users' Guide, 3rd edn. SIAM, Philadelphia (1999)
2. Benson, S.J.: Parallel computing on semidefinite programs. Technical report ANL/MCS-P939-0302, Argonne National Laboratory (2003)
3. Benson, S.J., Ye, Y.: DSDP3: Dual-scaling algorithm for semidefinite programming. Technical report ANL/MCS-P851-1000, Argonne National Laboratory (November 2001)
4. Blackford, L.S., Demmel, J., Dongarra, J., Duff, I., Hammarling, S., Henry, G., Heoux, M., Kaufman, L., Lumsdaine, A., Petitet, A., Pozo, R., Remington, K., Whaley, R.C.: An updated set of basic linear algebra subprograms (BLAS). ACM Trans. Math. Softw. 28(2), 135-151 (2002)
5. Borchers, B.: CSDP, a C library for semidefinite programming. Optim. Methods Softw. 11-2(1-4), 613-623 (1999)
6. Borchers, B.: SDPLIB 1.2, a library of semidefinite programming test problems. Optim. Methods Softw. 11-2(1-4), 683-690 (1999)
7. Burer, S., Choi, C.: Computational enhancements in low-rank semidefinite programming. University of Iowa (July 2004)
8. Burer, S., Monteiro, R.D.C.: A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization. Math. Program. 95(2), 329-357 (2003)
9. Chandra, R., Dagum, L., Kohr, D., Maydan, D., McDonald, J., Menon, R.: Parallel Programming in OpenMP. Morgan Kaufmann, New York (2000)
10. Czyzyk, J., Mesnier, M.P., Mor, J.J.: The NEOS server. IEEE Comput. Sci. Eng. 5(3), 68-75 (1998)
11. Fujisawa, K., Kojima, M., Nakata, K.: Exploiting sparsity in primal-dual interior-point methods for semidefinite programming. Math. Program. 79, 235-253 (1997)
12. Fukuda, M., Braams, B.J., Nakata, M., Overton, M.L., Percus, J.K., Yamashita, M., Zhao, Z.: Large-scale semidefinite programs in electronic structure calculation. Technical report B-413, Tokyo Institute of Technology, Department of Mathematical and Computing Sciences (February 2005)
13. Keuchel, J., Schnorr, C., Schellewald, C., Cremers, D.: Binary partitioning, perceptual grouping, and restoration with semidefinite programming. IEEE Trans. Pattern Anal. Mach. Intell. 25(11), 1364-1379 (2003)
14. Kocvara, M., Stingl, M.: Pennon: A code for convex nonlinear and semidefinite programming. Optim. Methods Softw. 18(3), 317-333 (2003)
15. Mittelmann, H.D.: An independent benchmarking of SDP and SOCP solvers. Math. Program. 95(2), 407-430 (2003)
16. Sturm, J.F.: Using sedumi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11-2(1-4), 625-653 (1999)
17. Sturm, J.F.: Implementation of interior point methods for mixed semidefinite and second order cone optimization problems. Optim. Methods Softw. 17(6), 1105-1154 (2002)
18. Toh, K.C., Todd, M.J., Tutuncu, R.H.: SDPT3 - a MATLAB software package for semidefinite programming, version 1.3. Optim. Methods Softw. 11-2(1-4), 545-581 (1999)
19. Tutuncu, R.H., Toh, K.C., Todd, M.J.: Solving semidefinite-quadratic- linear programs using SDPT3. Math. Program. 95(2), 189-217 (2003)
20. Yamashita, M., Fujisawa, K., Kojima, M.: Implementation and evaluation of SDPA 6.0 (semidefinite programming algorithm 6.0). Optim. Methods Softw. 18(4), 491-505 (2003)
21. Yamashita, M., Fujisawa, K., Kojima, M.: SDPARA: Semidefinite programming algorithm parallel version. Parallel Comput. 29, 1053-1067 (2003)