A Two-Cut Approach in the Analytic Center Cutting Plane Method

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 O ( n 2 " 2 ) calls to the oracle and that the recovery of a new analytic center can be done in O(1) primal damped Newton steps. Keywords Primal Newton algorithm, Analytic center, Cutting Plane Method, Two cuts. This work has been completed with the support from the Fonds National Suisse de la Recherche Scientifique, grant 12-42503.94, from the Natural Sciences and Engineering Research Council of Canada, grant number OPG0004152 and from the FCAR of Quebec. GERAD/Faculty of Management, McGill University, 1001, Sherbrooke West, Montreal, Que., H3A 1G5, Canada. E-mail: [email protected]. LOGILAB/Management Studies, University of Geneva, 102, Bd Carl-Vogt,..