-

 

 

 




Optimization Online





 

Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. VII. Inverse semigroup theory, closures, decomposition of perturbations

Robert Hildebrand (rhil***at***vt.edu)
Matthias Köppe (mkoeppe***at***math.ucdavis.edu)
Yuan Zhou (yuan.zhou***at***uky.edu)

Abstract: In this self-contained paper, we present a theory of the piecewise linear minimal valid functions for the 1-row Gomory-Johnson infinite group problem. The non-extreme minimal valid functions are those that admit effective perturbations. We give a precise description of the space of these perturbations as a direct sum of certain finite- and infinite-dimensional subspaces. The infinite-dimensional subspaces have partial symmetries; to describe them, we develop a theory of inverse semigroups of partial bijections, interacting with the functional equations satisfied by the perturbations. Our paper provides the foundation for grid-free algorithms for the Gomory-Johnson model, in particular for testing extremality of piecewise linear functions whose breakpoints are rational numbers with huge denominators.

Keywords: cutting planes, group relaxation, #cutgeneratingfunctionology

Category 1: Integer Programming (Cutting Plane Approaches )

Citation:

Download: [PDF]

Entry Submitted: 11/15/2018
Entry Accepted: 11/16/2018
Entry Last Modified: 01/05/2020

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society