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Primal–Dual–Infeasible Newton Approach for the Analytic Center Deep-Cutting Plane Method

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Abstract

The convergence and complexity of a primal–dual column generation and cutting plane algorithm from approximate analytic centers for solving convex feasibility problems defined by a deep cut separation oracle is studied. The primal–dual–infeasible Newton method is used to generate a primal–dual updating direction. The number of recentering steps is O(1) for cuts as deep as half way to the deepest cut, where the deepest cut is tangent to the primal–dual variant of Dikin's ellipsoid.

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Authors and Affiliations

  1. Faculty of Management, McGill University, Montreal, Quebec, Canada

    J. L. Goffin (Professor, GERAD)

  2. Faculty of Management, McGill University, Montreal, Quebec, Canada

    F. Sharifi-Mokhtarian (Post-Doctoral Fellow, GERAD)

Authors
  1. J. L. Goffin
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  2. F. Sharifi-Mokhtarian
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Goffin, J.L., Sharifi-Mokhtarian, F. Primal–Dual–Infeasible Newton Approach for the Analytic Center Deep-Cutting Plane Method. Journal of Optimization Theory and Applications 101, 35–58 (1999). https://doi.org/10.1023/A:1021714926231

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  • DOI: https://doi.org/10.1023/A:1021714926231

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