Algorithm 875: DSDP5-software for semidefinite programming

ACM Transactions on Mathematical Software

Volumn 34, Issue 3, 2008, Pages

  Benson, Steven J ^a   Ye, Yinyu ^b,c  

^a ARGONNE NATIONAL LABORATORY   (United States)

^b STANFORD UNIVERSITY   (United States)

^c Stanford University   (United States)

Author keywords

Conic programming; Dual scaling algorithm; Interior point methods; Linear matrix inequalities; Semidefinite programming

Indexed keywords

COMPUTATIONAL COMPLEXITY; DIGITAL LIBRARIES; LINEAR MATRIX INEQUALITIES; MATLAB; ROBUSTNESS (CONTROL SYSTEMS);

CONIC PROGRAMMING; DUAL SCALING ALGORITHMS; INTERIOR-POINT METHODS; SEMIDEFINITE PROGRAMMING;

COMPUTER SOFTWARE;

EID: 44249088324     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/1356052.1356057     Document Type: Article

References (48)

1. ANJOS, M. F. 2005. An improved semidefinite programming relaxation for the satisfiability problem. Math. Program. 102, 3, 589-608.
2. BATTISTA, G. D., ERLEBACH, T., HALL, A., PATRIGNANI, M., PIZZONIA, M., AND SCHANK, T. 2007. Computing the types of the relationships between autonomous systems. IEEE/ACM Trans. Netw. 15, 4, 1-16.
3. BENSON, S. J. AND YE, Y. 2005. DSDP5 user guide - software for semidefinite programming. Tech. rep. ANL/MCS-TM-277, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL. ftp://info.mcs.anl.gov/pub/tech_reports/reports/TM-277-complete. pdf.
4. BENSON, S. J., YE, Y., AND ZHANG, X. 1999. Mixed linear and semidefinite programming for combinatorial and quadratic optimization. Optim. Meth. Soft. 11, 515-544.
5. BENSON, S. J., YE, Y., AND ZHANG, X. 2000. Solving large-scale sparse semidefinite programs for combinatorial optimization. SIAM J. Optim. 10, 2, 443-461.
6. BERHAULT, M., HUANG, H., KESKINOCAK, P., KOENIG, S., ELMAGHRABY, W., GRIFFIN, P., AND KLEYWEGT, A. 2003. Robot exploration with combinatorial auctions. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Las Vegas, NV. 27-31.
7. BHARGAVA, A. AND KOSARAJU, S. 2003. Identifying Cell Cycle Regulatory Genes. Johns Hopkins University. http://www.cs.jhu.edu/∼ankur/.
8. BISWAS, P. AND YE, Y. 2004. Semidefinite programming for ad hoc wireless sensor network localization. In Proceedings of the 3rd International Symposium on Information Processing in Sensor Networks (IPSN). New York, NY, USA.
9. BORCHERS, B. 1999a. CSDP 2.3 user's guide. Optim. Meth. Softw. 11/12, 1-4, 597-611.
10. BORCHERS, B. 1999b. SDPLIB 1.2, a library of semidefinite programming test problems. Optimiz. Meth. Softw. 11, 683-690.
11. BURER, S. AND MONTEIRO, R. D. 2003. A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization. Math. Program. (Series B) 95, 2, 329-357.
12. CARTER, M., JIN, H., SAUNDERS, M., AND YE, Y. 2004. SPASELOC: An adaptive subproblem algorithm for scalable wireless network localization. Tech. rep., Stanford University. (Submitted to SIAM Journal of Optimization.)
13. DIMACS. 2000. Seventh DIMACS implementation challenge: Semidefinite and related optimization problems. Center for Discrete Mathematics and Theoretical Computer Science. http://dimacs.rutgers.edu/Challenges/Seventh/.
14. DOLAN, E. D. AND MORÉ, J. 2002. Benchmarking optimization software with performance profiles. Math. Program. 91, 201-213.
15. ENSTA. 2005. Optimisation combinatoire and recherche opé rationnelle. http://www.ensta.fr/∼diam/ao303/index.php.
16. FUJISAWA, K., KOJIMA, M., AND NAKATA, K. 1997. Exploiting sparsity in primal-dual interior-point methods for semidefinite programming. Math. Program. B79, 235-253.
17. GOEMANS, M. X. AND WILLIAMSON, D. P. 1995. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42 , 1115-1145.
18. GOLUB, G. H. AND VAN LOAN, C. F. 1989. Matrix Computations 2nd Ed. Johns Hopkins University Press, Baltimore, MD.
19. HELMBERG, C. AND RENDL, F. 2000. A spectral bundle method for semidefinite programming. SIAM J. Optimiz. 10, 3, 673-696.
20. HENRION, D. AND LASSERRE, J. B. 2003. GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi. ACM Trans. Math. Softw. 29, 2 , 165-194.
21. KEUCHEL, J., SCHELLEWALD, C., CREMERS, D., AND SCHNÖRR, C. 2001. Convex relaxations for binary image partitioning and perceptual grouping. In 23rd DAGM Symposium. Lecture Notes in Computer Science, S. F. e. B. Radig, Ed. vol. 2191. Springer, Berlin, Germany, 353-360.
22. KEUCHEL, J., SCHNÖRR, C., SCHELLEWALD, C., AND CREMERS, D. 2003. Binary partitioning, perceptual grouping, and restoration with semidefinite programming. IEEE Trans. Patt. Ana. Mach. Intell. 25, 11 (Special Issue on Energy Minimization Methods in Computer Vision and Pattern Recognition.) 1364-1379.
23. KISIALIOU, N. AND LUO, Z.-Q. SDR detector software package. http://www.ece.umn.edu/users/luozq/software/sw_about.html.
24. KOČVARA, M. AND STINGL, M. 2003. PENNON - a code for convex nonlinear and semidefinite programming. Optimiz. Meth. Softw. 18, 3, 317-333.
25. LI, X. AND JIANG, H. 2006. Solving large margin HMM estimation via semidefinite programming. In Proceedings of the 9th International Conference on Spoken Language Processing (ICSLP'06). Pittsburgh, PA. ISCA, Bonn, Germany.
26. LO̧FBERG, J. 2004. YALMIP: A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD Conference. Taipei, Taiwan. http://control.ee.ethz.ch/∼joloef/yalmip.php.
27. LU, F., KELEŞ, S., WRIGHT, S. J., AND WAHBA, G. 2005. Framework for kernel regularization with application to protein clustering. Proc. Nat. Acad. Sci. 102, 12332-12337.
28. MITTELMANN, H. D. 2005. Benchmarks for optimization software. http://plato.asu.edu/ftp/ {sdplib.html,sparse_sdp.html,dimacs_sdp.html}.
29. MOBASHER, A., TAHERZADEH, M., SOTIROV, R., AND KHANDANI, A. K. 2005. A near maximum likelihood decoding algorithm for MIMO systems based on semi-definite programming. Tech. rep. UW-E&CE#2005-12, Electrical and Computer Engineering Department, University of Waterloo, Waterloo, ON, Canada.
30. MORÉ, J. 2005. NEOS server for optimization. Mathematics and Computer Science Division, Argonne National Laboratory. http://www-neos.mcs. anl.gov/neos.
31. PRAJNA, S., PAPACHRISTODOULOU, A., SEILER, P., AND PARRILO, P. A. 2004. SOSTOOLS: Sum of squares optimization toolbox for MATLAB. http://www.cds.caltech.edu/sostools and http: //www.aut.ee.ethz.ch/∼parrilo/sostools.
32. RATSCHAN, S. 2004. Rsolver software package. http://rsolver.sourceforge.net/.
33. ROTEA, M. A. AND D'AMATO, F. J. 2001. LFTB: An optimized algorithm to bound worst-case frequency response functions. In Proceedings of the American Control Conference, Washington, DC. IEEE Computer Society, 3041-3048.
34. ROY, S. AND CHEN, W. 2005. Convexfit: an optimal minimum-error convex fitting and smoothing algorithm with application to gate-sizing. In Proceedings of the 2005 IEEE/ACM International Conference on Computer-Aided Design. (ICCAD '05). IEEE Computer Society, 196-203.
35. SCHRIJVER, A. 2005. New code upper bounds from the Terwilliger algebra and semidefinite programming. IEEE Trans. Info. Theory 51, 2859-2866.
36. SO, A. AND YE, Y. 2007. Theory of semidefinite programming for sensor network localization. Math. Program. 109, 2-3, 367-384.
37. STURM, J.F. 1999. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Meth. Softw. 11/12, 1-4, 625-653.
38. SZREBRO, N., RENNIE, J., AND JAAKKOLA, T. 2004. Maximum margin matrix factorization. http://people.csail.mit.edu/nati/mmmf/code.html.
39. TODD, M. J. 2001. Semidefinite Optimization. Vol. 10. Cambridge University Press, Cambridge, UK, 515-560.
40. TOH, K., TODD, M., AND TUTUNCU, R. 1999. SDPT3 - A Matlab software package for semidefinite programming, version 2.1. Optimiz. Meth. Softw. 11, 545-581.
41. TOH, K. C. 2002. A note on the calculation of step-lengths in interior-point methods for semidefinite programming. Comput. Optim. Appl. 21, 301-310.
42. WATSON, I. 2005. Private Communication. Eli Lilly and Company.
43. WOLKOWICZ, H., SAIGAL, R., AND VANDENBERGHE, L., Eds. 2000. Handbook of Semidefinite Programming. International Series in Operations Research and Management Science, vol. 27. Kluwer Academic Publishers.
44. YAMASHITA, M., FUJISAWA, K., AND KOJIMA, M. 2003. Implementation and evaluation of SDPA 6.0 (semidefinite programming algorithm 6.0). Optimiz. Meth. Softw. 18, 491-505.
45. YE, Y. 1997. Interior Point Algorithms: Theory and Analysis. Wiley-Interscience Series in Discrete Mathematics and Optimization. John Wiley & Sons, New York, NY.
46. YILDIRIM, E. A. AND FAN, X. 2005. On extracting maximum stable sets in perfect graphs using Lovasz's theta function. Comput. Optimiz. Appl. 32, 1-30.
47. ZHAO, Z., BRAAMS, B. J., FUKUDA, M., OVERTON, M. L., AND PERCUS, J. K. 2004. The reduced density matrix method for electronic structure calculations and the role of three-index representability. J. Chem. Phys. 120, 2095-2104.
48. ZOWE, J., KOČVARA, M., AND BENDSØE, M. 1997. Free material optimization via mathematical programming. Math. Program. 79, 445-466.