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