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Final Iterations in Interior Point Models -- Preconditioned Conjugate Gradients and Modified Search Directions

dc.contributor.authorWang, Weichungen_US
dc.description.abstractIn this article we consider modified search directions in the endgame of interior point methods for linear programming. In this stage, the normal equations determining the search directions become ill-conditioned. The modified search directions are computered by solving perturbed systems in which the systems may be solved efficiently by the preconditioned conjugate gradient solver. We prove the convergence of the interior point methods using the modified search directions and show that each barrier problem is solved with a superlinear convergence rate. A variation of Cholesky factorization is presented for computing a better preconditioner when the normal equations are ill-conditioned. These ideas have been implemented successfully and the numerical results show that the algorithms enhance the performance of the preconditioned conjugate gradients-based interior point methods.en_US
dc.format.extent289065 bytes
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3674en_US
dc.titleFinal Iterations in Interior Point Models -- Preconditioned Conjugate Gradients and Modified Search Directionsen_US
dc.typeTechnical Reporten_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtComputer Science Department Technical Reportsen_US

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