A two-cut approach in the analytic center cutting plane method

Abstract.

We analyze the two cut generation scheme in the analytic center cutting plane method. We propose an optimal updating direction when the two cuts are central. The direction is optimal in the sense that it maximizes the product of the new slacks within the trust region defined by Dikin's ellipsoid. We prove convergence in calls to the oracle and show that the recovery of a new analytic center can be done in O(1) primal damped Newton steps.