Strange Behaviors of Interior-point Methods for Solving Semidefinite Programming Problems in Polynomial Optimization

In this talk, we show that the standard SDP solvers, such as SeDuMi and SDPA, return the significantly wrong value as the optimal value for an SDP relaxation problem of a one-dimensional polynomial optimization problem, and provide some of the reason for this behavior. This numerical result gives a warning to be careful in believing the results of the SDP solvers. We also demonstrate that SDPA-GMP, a multiple precision SDP solver, can return the correct value as the optimal value.