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A central cutting plane algorithm for the convex programming problem

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Abstract

An algorithm is developed for solving the convex programming problem which iteratively proceeds to the optimum by constructing a cutting plane through the center of a polyhedral approximation to the optimum. This generates a sequence of primal feasible points whose limit points satisfy the Kuhn—Tucker conditions of the problem. Additionally, we present a simple, effective rule for dropping prior cuts, an easily calculated bound on the objective function, and a rate of convergence.

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Author notes

  1. Thomas G. Moore

    Present address: Bell Telephone Laboratories, Holmdel, N.J., USA

Authors and Affiliations

  1. The Johns Hopkins University, Baltimore, Maryland, USA

    Jack Elzinga & Thomas G. Moore

Authors
  1. Jack Elzinga
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  2. Thomas G. Moore
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Elzinga, J., Moore, T.G. A central cutting plane algorithm for the convex programming problem. Mathematical Programming 8, 134–145 (1975). https://doi.org/10.1007/BF01580439

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  • DOI: https://doi.org/10.1007/BF01580439

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