On the enumerative nature of Gomory’s dual cutting plane method

• Published in: Mathematical programming Vol. 125; no. 2; pp. 325 - 351
• Main Authors: Balas, Egon, Fischetti, Matteo, Zanette, Arrigo
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.10.2010; Springer; Springer Nature B.V
• Subjects: Algorithms; Applied sciences; Calculus of Variations and Optimal Control; Optimization; Combinatorics; Computation; Computational mathematics; Convergence; Cutting; Exact sciences and technology; Full Length Paper; Integer programming; Integers; Linear programming; Mathematical analysis; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematical programming; Mathematics; Mathematics and Statistics; Mathematics of Computing; Methods; Numerical Analysis; Operational research and scientific management; Operational research. Management science; Planes; Sound; Strategy; Studies; Theoretical; Cutting plane methods; 90C10 Integer programming; Computational analysis; Degeneracy in linear programming; 90C05 Linear programming; Lexicographic dual simplex; Gomory cuts; 90C49 Extreme-point and pivoting methods; Belief; Branching; Pivoting method; Computational analysis 90C 10 Integer programming; Multicriteria analysis; Branch and bound method; Degenerate system; Linear programming; Cutting plane method; Cut generation; Integer programming; Extremum; Lexicography; Lexicographic order; Objective function; Mathematical programming
• ISSN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-010-0392-4

For 30 years after their invention half a century ago, cutting planes for integer programs have been an object of theoretical investigations that had no apparent practical use. When they finally proved their practical usefulness in the late eighties, that happened in the framework of branch and boun...