We investigate ill-posed semidefinite programming problems for which Slater's constraint qualifications fail, and propose a new reliable termination criterium dealing with such problems. This criterium is scale-independent and provides verified forward error bounds for the true optimal value, where all rounding errors due to floating point arithmetic are taken into account. It is based on a boundedness qualification, which is satisfied for many problems. Numerical experiments, including combinatorial problems, are presented.
Informatik III, TU Hamburg-Harburg, Schwarzenbergstr. 95, 21073 Hamburg, submitted