A geometric approach to cut-generating functions

The cutting-plane approach to integer programming was initiated more than 40 years ago: Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau form and Balas introduced intersection cuts for the corner polyhedron. This line of research was left dormant for several...

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Bibliographic Details
Published in:Mathematical programming 2015-06, Vol.151 (1), p.153-189
Main Authors: Basu, Amitabh, Conforti, Michele, Di Summa, Marco
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Convex analysis
Euclidean space
Full Length Paper
Geometry
Integer programming
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Optimization techniques
Studies
Theoretical
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Summary:The cutting-plane approach to integer programming was initiated more than 40 years ago: Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau form and Balas introduced intersection cuts for the corner polyhedron. This line of research was left dormant for several decades until relatively recently, when a paper of Andersen, Louveaux, Weismantel and Wolsey generated renewed interest in the corner polyhedron and intersection cuts. Recent developments rely on tools drawn from convex analysis, geometry and number theory, and constitute an elegant bridge between these areas and integer programming. We survey these results and highlight recent breakthroughs in this area.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-015-0890-5