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How to Extend the Concept of Convexity Cuts to Derive Deeper Cutting Planes

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Abstract

A new type of cutting plane, termed a decomposition cut, is introduced that can be constructed under the same assumptions as the well-known convexity cut. Therefore it can be applied in algorithms (e.g. cutting plane, branch-and-cut) for various problems of global optimization, such as concave minimization, bilinear programming, reverse-convex programming, and integer programming. In computational tests with cutting plane algorithms for concave minimization, decomposition cuts were shown to be superior to convexity cuts.

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Authors and Affiliations

  1. Department of Economics and Business Administration, Philipps-University, Marburg, Germany

    Marcus Porembski

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  1. Marcus Porembski
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Porembski, M. How to Extend the Concept of Convexity Cuts to Derive Deeper Cutting Planes. Journal of Global Optimization 15, 371–404 (1999). https://doi.org/10.1023/A:1008315229750

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  • DOI: https://doi.org/10.1023/A:1008315229750

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