A general framework for cutting-plane generation was proposed by Applegate et al. in the context of the traveling salesman problem. The process considers the image of a problem space under a linear mapping, chosen so that a relaxation of the mapped problem can be solved efficiently. Optimization in the mapped space can be used to find a separating hyperplane, if one exists, and via substitution this gives a cutting plane in the original space. We extend this procedure to general mixed-integer programming problems, obtaining a range of possibilities for new sources of cutting planes. Some of these possibilities are explored computationally, both in floating-point arithmetic and in rational arithmetic. © 2013 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.
CITATION STYLE
Chvátal, V., Cook, W., & Espinoza, D. (2013). Local cuts for mixed-integer programming. Mathematical Programming Computation, 5(2), 171–200. https://doi.org/10.1007/s12532-013-0052-9
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