1 Apr 2008 ===================================================== Several SDP-codes on SDP problems with free variables ===================================================== Hans D. Mittelmann (mittelmann@asu.edu)
The URL of this benchmark is: http://plato.asu.edu/ftp/sdp_free.html
Logfiles for these runs are at: http://plato.asu.edu/ftp/sdp_free_logs/
CSDP-5.0: http://www.nmt.edu/~borchers/csdp.html
SDPT3-4.0-beta: http://www.math.nus.edu.sg/~mattohkc/sdpt3.html
SeDuMi-1.1: http://sedumi.mcmaster.ca
SDPA-7.10: http://homepage.mac.com/klabtitech/sdpa-homepage/
These codes were used to solve SDP problems with free variables from
http://plato.asu.edu/ftp/sdp_free/ (see README)
The codes were run in default mode on a 12GB 2.4 GHz 64-bit dual-processor Opteron under Linux. For all codes the maximum of the six error measures is given as defined in the 7th DIMACS Challenge benchmark paper Math Prog 95, 407-430 (2003), http://plato.asu.edu/dimacs/node3.html.
In the second table CPU user times are given, with the elapsed time for CSDP2 which is CSDP compiled with -lpthread, to be replaced by OpenMP version when gcc-4.2 is released. ATLAS is used by CSDP and SDPA.
Input to SeDuMi and SDPT3 in Matlab while CSDP and SDPA were fed sparse SDPA format files in which free variables were replaced by the difference of two nonnegative variables.
========================================================== problem SeDuMi SDPT3 SeDuMif CSDP SDPA ---------------------------------------------------------- q_17_0.5_1 1.9e-07 2.8e-07 1.3e-06 1.3e-08 2.8e-05 q_17_0.5_2 8.8e-07 3.7e-09 5.3e-07 6.9e-09 2.3e-06 q_17_0.5_3 7.6e-09 9.7e-09 1.4e-08 1.2e-08 3.8e-06 q_17_0.5_4 1.9e-06 7.1e-07 1.5e-06 4.9e-08 8.3e-06 q_17_0.5_5 1.6e-06 6.0e-09 1.7e-07 1.0e-08 1.6e-06 q_17_0.5_6 1.6e-07 3.2e-08 2.1e-07 2.0e-08 3.3e-06 q_17_0.5_7 2.3e-09 7.2e-09 1.8e-07 4.3e-08 8.6e-07 q_17_0.5_8 8.7e-08 3.8e-09 1.0e-06 4.4e-09 2.0e-06 q_17_0.5_9 8.5e-09 8.8e-09 1.9e-06 2.2e-08 6.1e-06 q_17_0.5_10 2.1e-07 1.5e-08 9.5e-09 5.0e-09 1.6e-07 ---------------------------------------------------------- s_17_0.5_1 2.3e-07 3.7e-08 1.4e-07 9.7e-09 6.7e-06 s_17_0.5_2 7.2e-08 1.3e-05 4.4e-08 1.2e-09 6.5e-06 s_17_0.5_3 1.6e-07 3.8e-07 2.4e-07 6.9e-09 8.0e-06 s_17_0.5_4 4.3e-07 8.7e-05 1.6e-07 7.5e-09 9.5e-06 s_17_0.5_5 5.3e-07 1.9e-05 2.8e-07 2.2e-09 9.1e-06 s_17_0.5_6 2.3e-07 1.1e-05 1.1e-07 6.6e-09 1.2e-05 s_17_0.5_7 4.4e-07 1.8e-05 4.7e-07 5.0e-09 1.1e-05 s_17_0.5_8 6.4e-08 1.1e-08 1.2e-07 6.4e-09 9.5e-06 s_17_0.5_9 3.7e-07 1.2e-05 3.7e-08 3.8e-09 6.9e-06 s_17_0.5_10 4.6e-08 1.5e-07 1.3e-08 1.2e-09 6.6e-06 ---------------------------------------------------------- MaxC_100_1 1.0e-09 2.5e-08 1.3e-10 8.2e-08 6.5e-06 MaxC_100_2 1.0e-09 2.5e-08 1.3e-10 8.2e-08 6.5e-06 MaxC_100_3 1.1e-09 8.7e-08 2.1e-09 6.8e-08 1.7e-05 MaxC_100_4 4.7e-09 5.7e-07 4.1e-10 1.6e-08 1.0e-05 MaxC_100_5 3.0e-09 3.4e-06 2.0e-09 3.9e-07 5.0e-06 MaxC_100_6 9.8e-10 2.2e-08 2.2e-09 3.1e-08 1.9e-05 MaxC_100_7 1.7e-09 5.2e-06 1.1e-08 3.1e-08 9.6e-06 MaxC_100_8 5.5e-09 4.0e-08 3.0e-09 1.8e-08 5.6e-06 MaxC_100_9 4.1e-10 1.1e-08 8.0e-09 2.0e-08 4.8e-06 MaxC_100_10 8.0e-09 1.5e-07 1.0e-08 2.1e-08 1.8e-05 ---------------------------------------------------------- Maximum of the DIMACS error measures, SeDuMif: pars.free=0 ============================================================== problem SeDuMi SDPT3 SeDuMif CSDP CSDP2 SDPA -------------------------------------------------------------- q_17_0.5_1 4831 1390 4380 1546 1218 7614 q_17_0.5_2 5162 1137 4945 1325 1057 568 q_17_0.5_3 5355 932 5127 1305 994 653 q_17_0.5_4 4755 1394 4356 1720 1380 541 q_17_0.5_5 5047 985 4736 1315 1023 611 q_17_0.5_6 5162 1184 4735 1129 914 697 q_17_0.5_7 4181 691 3977 998 804 552 q_17_0.5_8 3988 793 4168 1042 849 640 q_17_0.5_9 5117 1105 4737 1246 991 640 q_17_0.5_10 4953 828 5137 1157 929 1396 -------------------------------------------------------------- s_17_0.5_1 2366 806 2560 718 544 663 s_17_0.5_2 3292 857 3588 833 633 720 s_17_0.5_3 2570 1076 2579 770 550 662 s_17_0.5_4 3937 969 4274 946 712 749 s_17_0.5_5 3503 988 3676 841 632 720 s_17_0.5_6 3676 995 3853 869 655 635 s_17_0.5_7 3411 975 3806 942 669 721 s_17_0.5_8 2258 768 2559 729 554 635 s_17_0.5_9 3697 1230 3784 832 635 721 s_17_0.5_10 3146 929 3442 880 622 691 -------------------------------------------------------------- MaxC_100_1 548 147 27 844 590 23 MaxC_100_2 612 145 27 853 588 23 MaxC_100_3 737 575 52 1516 1011 55 MaxC_100_4 709 126 33 748 550 18 MaxC_100_5 724 328 43 1969 1207 37 MaxC_100_6 460 168 26 725 480 27 MaxC_100_7 1149 433 54 1890 1103 41 MaxC_100_8 612 457 39 1510 912 45 MaxC_100_9 578 214 32 1029 655 39 MaxC_100_10 998 519 110 1579 1090 54 ------------------------------------------------------------- CPU times in seconds ================================================= problem constr vars free blocks ------------------------------------------------- s_17_0.5_* 5984 477 272 18 q_17_0.5_* 5984 189 2907 2 ------------------------------------------------- MaxC_100_1 6252 1850 2094 79 MaxC_100_2 6252 1850 2094 79 MaxC_100_3 7767 2134 2295 79 MaxC_100_4 5679 1775 1938 82 MaxC_100_5 6717 1877 2238 77 MaxC_100_6 6059 1759 2022 77 MaxC_100_7 7221 2103 2450 80 MaxC_100_8 7375 2121 2200 81 MaxC_100_9 6495 1937 2164 82 MaxC_100_10 7228 1923 2408 74 ------------------------------------------------- Problem sizes