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

Authors:
Marcus Porembski
Affiliations:
Department of Economics and Business Administration, Philipps-University, Marburg, Germany
Venue:
Journal of Global Optimization
Year:
1999

Citing 7
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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.