This is a collection of sparse linear SDP problems arising in structural optimization. While the `trto' problems are `academic' (they can be reformulated as LP and solved much more efficiently), the other problems have important engineering background.
problem group | size (KB) |
mater.zip | 14,236 |
buck.zip | 311 |
shmup.zip | 863 |
trto.zip | 151 |
vibra.zip | 289 |
problem | n | m | objective |
mater-1 | 103 | 222 | -1.434654e+02 |
mater-2 | 423 | 1014 | -1.415919e+02 |
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 |
trto1 | 36 | 25+36 | 1.1045 (exact value) |
trto2 | 144 | 91+144 | 1.28 (exact value) |
trto3 | 544 | 312+544 | 1.28 (exact value) |
trto4 | 1200 | 673+1200 | 1.276582 |
trto5 | 3280 | 1761+3280 | 1.28 (exact value) |
buck1 | 36 | 49+36 | 14.64192 |
buck2 | 144 | 193+144 | 292.3683 |
buck3 | 544 | 641+544 | 607.6055 |
buck4 | 1200 | 1345+1200 | 486.1421 |
buck5 | 3280 | 3521+3280 | 436.2390 |
vibra1 | 36 | 49+36 | 40.81901 |
vibra2 | 144 | 193+144 | 166.0153 |
vibra3 | 544 | 641+544 | 172.6130 |
vibra4 | 1200 | 1345+1200 | 165.6133 |
vibra5 | 3280 | 3521+3280 | 165.9029 |
shmup1 | 16 | 81+32 | 188.4148 |
shmup2 | 200 | 881+400 | 3462.427 |
shmup3 | 420 | 1801+840 | 2098.838 |
shmup4 | 800 | 3361+1600 | 7992.534 |
shmup5 | 1800 | 7441+3600 | 23858.867 |
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.
In the `mater' problems, the constraint matrix contains many small blocks.
In all other problems, the constraint matrix contains two (in `trto' one)
sparse diagonal blocks.
The optimal objective values were computed by PENSDP and, in most cases,
confirmed by SDPT3 and MOSEK. In the large-scale problems, the two/three
codes may differ in the 5th-6th digit. In this case, we give the PENSDP
value.
`mater' are problems of multiple-load free material
optimization (area of structural optimization) modeled by linear SDP as
described in [1]. All six examples solve the same problem (geometry,
loads, boundary conditions) and differ only in the finite element
discretization.
`trto' are problems from single-load truss topology
design. Normally formulated as LP, here reformulated as SDP for testing
purposes. (see, eg, [2],[3])
`vibra' are single load truss topology problems with a
vibration constraint. The constraint guarantees that the minimal
self-vibration frequency of the optimal structure is bigger than a given
value; see [4].
`buck' are single load truss topology problems with
linearized global buckling constraint. Originally a nonlinear matrix
inequality, the constraint should guarantee that the optimal structure is
mechanically stable (it doesn't buckle); see [4].
`shmup' are minimum volume, single load free material
optimization problems [5] with a vibration constraint and upper bound on
the material density. The vibration constraint guarantees that the minimal
self-vibration frequency of the optimal structure is bigger than a given
value.