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On the Convergence of Cone Splitting Algorithms with ω-Subdivisions

Author

Listed:
  • B. Jaumard

    (GERAD and École Polytechnique de Montréal)

  • C. Meyer

    (École Polytechnique de Montréal)

Abstract

We present a convergence proof of the Tuy cone splitting algorithm with a pure ω-subdivision strategy for the minimization of a concave function over a polytope. The key idea of the convergence proof is to associate with the current hyperplane a new hyperplane that supports the whole polytope instead of only the portion of it contained in the current cone. A branch-and-bound variant of the algorithm is also discussed.

Suggested Citation

  • B. Jaumard & C. Meyer, 2001. "On the Convergence of Cone Splitting Algorithms with ω-Subdivisions," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 119-144, July.
    • Handle: RePEc:spr:joptap:v:110:y:2001:i:1:d:10.1023_a:1017595513275
    DOI: 10.1023/A:1017595513275
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    References listed on IDEAS

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    1. Philip B. Zwart, 1974. "Global Maximization of a Convex Function with Linear Inequality Constraints," Operations Research, INFORMS, vol. 22(3), pages 602-609, June.
    2. Nguyen Van Thoai & Hoang Tuy, 1980. "Convergent Algorithms for Minimizing a Concave Function," Mathematics of Operations Research, INFORMS, vol. 5(4), pages 556-566, November.
    3. Philip B. Zwart, 1973. "Nonlinear Programming: Counterexamples to Two Global Optimization Algorithms," Operations Research, INFORMS, vol. 21(6), pages 1260-1266, December.
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