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)|
|trto1||36||25+36||1.1045 (exact value)|
|trto2||144||91+144||1.28 (exact value)|
|trto3||544||312+544||1.28 (exact value)|
|trto5||3280||1761+3280||1.28 (exact value)|
n is the number of variables, m the size
of the matrix constraint 25+36 means: matrix constraint of size 25 and 36
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 . 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, ,)
`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 .
`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 .
`shmup' are minimum volume, single load free material optimization problems  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.