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...

Abstract In this paper we present general-purpose preconditioners for regularized augmented systems, and their corresponding normal equations, arising from optimization problems. We discuss positive definite preconditioners, suitable CG MINRES. consider “sparsifications" which avoid situations in eigenvalues of the preconditioned matrix may become complex. Special attention is given to systems ...