Results of mater problems
This set contains examples from multiple-load free material optimization
modeled by linear SDP as described in Ben-Tal-Kocvara-Nemirovski-Zowe.
All examples solve the same problem (geometry, loads, boundary conditions)
and differ only in the finite element discretization.
The linear matrix operator A = sum Ai xi
has block diagonal structure with many small (11 x 11 - 20 x 20) blocks. Moreover,
only few
(6 - 12) of these blocks are nonzero in any Ai. As
a result, the Hessian of the augmented Lagrangian associated with
this problem is a large and sparse matrix.
Problem dimensions
| problem |
n |
m |
optimal_value |
| mater-3 |
1439 |
3588 |
-1.339163e+02 |
| mater-4 |
4807 |
12498 |
-1.342627e+02 |
| mater-5 |
10143 |
26820 |
-1.338016e+02 |
| mater-6 |
20463 |
56311 |
-1.335387e+02 |
Results
problem
|
SDPT3 |
|
CSDP |
|
SeDuMi |
|
PENNON |
|
|
CPU |
s |
CPU |
s |
CPU |
s |
CPU |
s |
| mater-3 |
35 |
6 |
19 |
7 |
20 |
7 |
7 |
7 |
| mater-4 |
295 |
5 |
409 |
7 |
97 |
7 |
32 |
7 |
| mater-5 |
memory |
|
3551 |
7 |
202 |
7 |
89 |
7 |
| mater-6 |
memory |
|
memory |
|
533 |
7 |
277 |
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.
"memory" means the code/problem did not fit in the available memory
Michal
Kocvara
June 27, 2003