Results of truss problems

We solve problems from truss topology design: All problems from this set are characterized by sparsity of the linear matrix operato A. From all the tested SDP solvers, only SDPT3 and PENNON, followed by SDPA, could solve them efficiently. All the other codes needed at least five times more CPU time to solve the large problems.

Problem dimensions

problem n m Optimal value
trto3 544 321+544 1.28 (e)
trto4 1200 673+1200 1.276582
trto5 3280 1761+3280 1.28 (e)
buck3 544 641+544 607.6055
buck4 1200 1345+1200 486.1421
buck5 3280 3521+3280 436.2292
vibra3 544 641+544 172.6130
vibra4 1200 1345+1200 165.6133
vibra5 3280 3521+3280 165.9029
(e) denotes known exact optimal value;
n is the number of variables, m the size of the matrix constraint;
25+36 means: matrix constraint of size 25 and 36 linear constraints

Results

problem SDPA
SDPT3
PENNON

CPU s CPU s CPU s
trto3 18 6 19 7 18 7
trto4 186 6 124 6 113 7
trto5 2808 5 1422 5 1575 7
buck3 36 6 43 4 40 7
buck4 369 6 241 7 229 7
buck5 7305 5 2766 7 3131 5
vibra3 49 5 45 5 34 7
vibra4 399 7 294 6 199 7
vibra5 7313 7 3601 5 2810 7

Test performed on Pentium IV PC (2.5 GHz) with 2GB RDRAM running Linux-2.4.19.
"s" is the number of digits of accuracy, CPU in seconds.


Michal Kocvara
June 27, 2003