Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. VI. The curious case of two-sided discontinuous minimal valid functions

Matthias Köppe; Yuan Zhou

Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. VI. The curious case of two-sided discontinuous minimal valid functions

Optimization and Control 2018-02-06 v3

Authors: Matthias Köppe , Yuan Zhou

Abstract

We construct a two-sided discontinuous piecewise linear minimal valid function for the 1-row Gomory--Johnson model which is not extreme, but which is not a convex combination of other piecewise linear minimal valid functions. The new function only admits piecewise microperiodic perturbations. We present an algorithm for computations with a restricted class of such perturbations.

Keywords

Gomory-Johnson model infinite group problem minimal valid function equivariant perturbation piecewise linear two-sided discontinuous microperiodic perturbation

Cite

@article{arxiv.1605.03975,
  title  = {Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. VI. The curious case of two-sided discontinuous minimal valid functions},
  author = {Matthias Köppe and Yuan Zhou},
  journal= {arXiv preprint arXiv:1605.03975},
  year   = {2018}
}

Comments

28 pages, 5 figures. v3: corrected Thm. 3.1, lemma in App. B, and proof of Thm. 5.1

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