Solving SDP Completely with an Interior Point Oracle

Understand

We suppose the existence of an oracle which solves any semidefinite programming (SDP) problem satisfying Slater's condition simultaneously at its primal and dual sides.

• We note that such an oracle might not be able to directly solve general SDPs even after certain regularization schemes are applied.
• In this work we fill this gap and show how to use such an oracle to "completely solve" an arbitrary SDP.
• Completely solving an SDP, includes, for example, distinguishing between weak/strong feasibility/infeasibility and detecting when the optimal value is attained or not.