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Approximation of Minimal Functions by Extreme Functions

Teresa Lebair(tlebair1***at***jhu.edu)
Amitabh Basu(basu.amitabh***at***jhu.edu)

Abstract: In a recent paper, Basu, Hildebrand, and Molinaro established that the set of continuous minimal functions for the 1-dimensional Gomory-Johnson infinite group relaxation possesses a dense subset of extreme functions. The n-dimensional version of this result was left as an open question. In the present paper, we settle this query in the affirmative: for any integer $n \geq 1$, every continuous minimal function can be arbitrarily well approximated by an extreme function in the n-dimensional Gomory-Johnson model.

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

Category 1: Integer Programming (Cutting Plane Approaches )


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

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