Equivariant perturbation in Gomory and Johnson's infinite group problem. VI: The curious case of two-sided discontinuous minimal valid functions

DOI10.1016/j.disopt.2018.05.003zbMath1454.90034arXiv1605.03975OpenAlexW2962802259MaRDI QIDQ1756343

Matthias Köppe, Yuan Zhou

Publication date: 14 January 2019

Published in: Discrete Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.03975

zbMATH Keywords

cutting planesinteger programscut-generating functionsgroup relaxations

Mathematics Subject Classification ID

Mixed integer programming (90C11) Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57)

Related Items

Equivariant perturbation in Gomory and Johnson's infinite group problem (V). Software for the continuous and discontinuous 1-row case, Facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem, An extreme function which is nonnegative and discontinuous everywhere, Dual-feasible functions for integer programming and combinatorial optimization: algorithms, characterizations, and approximations, Equivariant perturbation in Gomory and Johnson's infinite group problem. VII: Inverse semigroup theory, closures, decomposition of perturbations

Uses Software

• SageMath
• infinite group relaxation
• GitHub

Cites Work

• Light on the infinite group relaxation. I: Foundations and taxonomy
• A counterexample to a conjecture of Gomory and Johnson
• Equivariant perturbation in Gomory and Johnson's infinite group problem. III: Foundations for the \(k\)-dimensional case with applications to \(k=2\)
• On the extreme inequalities of infinite group problems
• Valid inequalities for mips and group polyhedra from approximate liftings
• Strengthening Chvátal-Gomory cuts and Gomory fractional cuts
• Extreme functions with an arbitrary number of slopes
• On the notions of facets, weak facets, and extreme functions of the Gomory-Johnson Infinite Group problem
• Some polyhedra related to combinatorial problems
• Valid inequalities based on simple mixed-integer sets
• Software for Cut-Generating Functions in the Gomory–Johnson Model and Beyond
• Equivariant perturbation in Gomory and Johnson's infinite group problem (V). Software for the continuous and discontinuous 1-row case
• Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. I. The One-Dimensional Case
• Some continuous functions related to corner polyhedra
• Some continuous functions related to corner polyhedra, II