Solving SDP completely with an interior point oracle

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. note that such might not be able to directly solve general SDPs even after certain regularization schemes are applied. In this work we fill gap show how use "completely solve" arbitrary SDP. Completely solving SDP, includes, for example, distinguishing between weak/strong feasibility/infeasibility detecting when optimal value is attained or not. will employ several tools, including a variant facial reduction where all auxiliary problems ensured satisfy Our main technical innovation, however, analysis double reduction, process applying twice: first original then once more regularized obtained during run. Although our discussion focused on programming, majority results proved convex cones