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

Author

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  • Jean-Louis Goffin
  • Jean-Philippe Vial

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. Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • Jean-Louis Goffin & Jean-Philippe Vial, 1999. "A two-cut approach in the analytic center cutting plane method," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(1), pages 149-169, March.
    • Handle: RePEc:spr:mathme:v:49:y:1999:i:1:p:149-169
    DOI: 10.1007/s186-1999-8372-7
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