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Cutting-Plane Methods without Nested Constraint Sets

Author

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  • Donald M. Topkis

    (University of California, Berkeley, California)

Abstract

This paper gives general conditions for the convergence of a class of cutting-plane algorithms without requiring that the constraint sets for the sub-problems be sequentially nested. Conditions are given under which inactive constraints may be dropped after each subproblem. Procedures for generating cutting-planes include those of Kelley, Cheney and Goldstein, and a generalization of the one used by both Zoutendijk and Veinott. For algorithms with nested constraint sets, these conditions reduce to a special case of those of Zangwill for such problems and include as special cases the algorithms of Kelley, Cheney and Goldstein, and Veinott. Finally, the paper gives an arithmetic convergence rate.

Suggested Citation

  • Donald M. Topkis, 1970. "Cutting-Plane Methods without Nested Constraint Sets," Operations Research, INFORMS, vol. 18(3), pages 404-413, June.
    • Handle: RePEc:inm:oropre:v:18:y:1970:i:3:p:404-413
    DOI: 10.1287/opre.18.3.404
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    Cited by:

    1. Frederic H. Murphy, 1972. "Row Dropping Procedures for Cutting Plane Algorithms," Discussion Papers 16, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Valerian Bulatov, 2010. "Methods of embedding-cutting off in problems of mathematical programming," Journal of Global Optimization, Springer, vol. 48(1), pages 3-15, September.

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