This page contains SDP relaxation problems in our papers:

• H. Waki, M. Nakata and M. Muramatsu, "Strange Behaviors of Interior-point Methods for Solving Semidefinite Programming Problems in Polynomial Optimization", Computational Optimization and Applications, Vol. 53 (3) 823--844 (2012)
• H. Waki, "How to generate weakly infeasible semidefinite programs via Lasserre's relaxations for polynomial optimization", Optimization Letters, Vol. 6 (8) 1883-1896 (2012)

The file ``unboundedDim1.tar.gz" contains SDP problems with sdpa format which are solved in the first paper. In the first paper, we mentioned that the standard SDP solvers, such as SeDuMi, SDPA, CSDP and SDPT3, return the wrong values "1" as the optimal value for SDP problems ``unboundDim1R*.dat-s". In contrast, SDPA-GMP returns the correct value "0".

The file ``CompactDim2.tar.gz" contains SDP problems with sdpa format which are solved in the second paper. In the second paper, we mentioned that all the standard SDP solvers which SDPA-GMP, return the wrong values "-1.5" as the optimal value for SDP problems ``Compact2DimPOPr*.dat-s". In contrast, all the problems are weakly infeasible and their duals are unbounded.

If you are interesting in these results in our paper, please challenge to solve SDP problems attached in this page by your SDP solver. And, if you can find the correct value by your algorithms and/or solvers, please let us know.

Written by Hayato Waki (2013-04-09)