A preconditioned iterative interior point approach to the conic bundle subproblem

Abstract The conic bundle implementation of the spectral method for large scale semidefinite programming solves in each iteration a quadratic subproblem by an interior point approach. For larger cutting model sizes limiting operation is collecting and factorizing Schur complement primal-dual KKT system. We explore possibilities to improve on this iterative approach that exploits structural low rank properties. Two preconditioning approaches are proposed analyzed. Both might be interest structured positive definite systems general. first employs projections onto random subspaces, second projects subspace chosen deterministically based both theoretic bounds derived associated condition number. In instances tested deterministic preconditioner provides surprisingly efficient control actual results suggest solver usually better choice if precision requirements moderate or size complemented system clearly exceeds active dimension within giving rise method.