The structure of the infinite models in integer programming

DOI10.1007/978-3-319-59250-3_6zbMath1418.90159arXiv1612.06288OpenAlexW2567243653WikidataQ127437975 ScholiaQ127437975MaRDI QIDQ2401145

Michele Conforti, Marco Di Summa, Joseph Paat, Amitabh Basu

Publication date: 31 August 2017

Published in: Mathematics of Operations Research (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.06288

zbMATH Keywords

cut-generating functionsGomory-Johnson infinite relaxation

Mathematics Subject Classification ID

Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Integer programming (90C10) Mixed integer programming (90C11) Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Related Items

The structure of the infinite models in integer programming, Optimal Cutting Planes from the Group Relaxations, Approximation of Minimal Functions by Extreme Functions, Nonunique Lifting of Integer Variables in Minimal Inequalities, Facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem, Piecewise smooth extreme functions are piecewise linear, An extreme function which is nonnegative and discontinuous everywhere

Uses Software

• infinite group relaxation

Cites Work

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• Light on the infinite group relaxation. I: Foundations and taxonomy
• On sublinear inequalities for mixed integer conic programs
• Sufficiency of cut-generating functions
• On the extreme inequalities of infinite group problems
• Equivalence between intersection cuts and the corner polyhedron
• On degenerate multi-row Gomory cuts
• Strengthening Chvátal-Gomory cuts and Gomory fractional cuts
• An electronic compendium of extreme functions for the Gomory-Johnson infinite group problem
• A geometric approach to cut-generating functions
• The structure of the infinite models in integer programming
• Some polyhedra related to combinatorial problems
• Valid inequalities based on simple mixed-integer sets
• On Minimal Valid Inequalities for Mixed Integer Conic Programs
• Cut-Generating Functions for Integer Variables
• Maximal Lattice-Free Convex Sets in Linear Subspaces
• Integer Programming
• Operations that Preserve the Covering Property of the Lifting Region
• New inequalities for finite and infinite group problems from approximate lifting
• On the existence of optimal solutions to integer and mixed-integer programming problems
• Some continuous functions related to corner polyhedra
• Some continuous functions related to corner polyhedra, II