Optimization Online


Optimal cutting planes from the group relaxations

Amitabh Basu(basu.amitabh***at***jhu.edu)
Michele Conforti(conforti***at***math.unipd.it)
Marco Di Summa(disumma***at***math.unipd.it)

Abstract: We study quantitative criteria for evaluating the strength of valid inequalities for Gomory and Johnson's finite and infinite group models and we describe the valid inequalities that are optimal for these criteria. We justify and focus on the criterion of maximizing the volume of the nonnegative orthant cut off by a valid inequality. For the finite group model of prime order, we show that the unique maximizer is an automorphism of the {\em Gomory Mixed-Integer (GMI) cut} for a possibly {\em different} finite group problem of the same order. We extend the notion of volume of a simplex to the infinite dimensional case. This is used to show that in the infinite group model, the GMI cut maximizes the volume of the nonnegative orthant cut off by an inequality.

Keywords: cutting planes, integer programming, Gomory-Johnson infinite relaxations

Category 1: Integer Programming (Cutting Plane Approaches )


Download: [PDF]

Entry Submitted: 10/23/2017
Entry Accepted: 10/24/2017
Entry Last Modified: 10/23/2017

Modify/Update this entry

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


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