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On the hierarchy of γ‐valid cuts in global optimization

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  • Marcus Porembski

Abstract

Concavity Cuts play an important role in concave minimization. In Porembski, J Global Optim 15 (1999), 371–404 we extended the concept underlying concavity cuts which led to the development of decomposition cuts. In numerical experiments with pure cutting plane algorithms for concave minimization, decomposition cuts have been shown to be superior to concavity cuts. However, three points remained open. First, how to derive decomposition cuts in the degenerate case. Second, how to ensure dominance of decomposition cuts over concavity cuts. Third, how to ensure the finite convergence of a pure cutting plane algorithm solely by decomposition cuts. These points will be addressed in this paper. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008

Suggested Citation

  • Marcus Porembski, 2008. "On the hierarchy of γ‐valid cuts in global optimization," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(1), pages 1-15, February.
    • Handle: RePEc:wly:navres:v:55:y:2008:i:1:p:1-15
    DOI: 10.1002/nav.20257
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    References listed on IDEAS

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    1. Kurt M. Bretthauer & A. Victor Cabot & M. A. Venkataramanan, 1994. "An algorithm and new penalties for concave integer minimization over a polyhedron," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 435-454, April.
    2. Harold P. Benson, 1996. "Deterministic algorithms for constrained concave minimization: A unified critical survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 765-795, September.
    3. Fred Glover, 1973. "Convexity Cuts and Cut Search," Operations Research, INFORMS, vol. 21(1), pages 123-134, February.
    4. Kurt M. Bretthauer, 1994. "A penalty for concave minimization derived from the tuy cutting plane," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 455-463, April.
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