Algorithmic and modeling insights via volumetric comparison of polyhedral relaxations

Jon Lee, Daphne E Skipper, Emily Speakman

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

This is mostly a survey on some mathematical results concerning volumes of polytopes of interest in non-convex optimization. Our motivation is in geometrically comparing relaxations in the context of mixed-integer linear and nonlinear optimization, with the goal of gaining algorithmic and modeling insights. We consider relaxations of: fixed-charge formulations, vertex packing polytopes, boolean-quadric polytopes, and relaxations of graphs of monomials on box domains. Besides surveying the area, we do give a few new results, and we provide many directions for further work.

Original languageEnglish (US)
Pages (from-to)121-140
Number of pages20
JournalMathematical Programming
Volume170
Issue number1
DOIs
StatePublished - Jul 1 2018

Fingerprint

Polytopes
Surveying
Modeling
Linear Optimization
Nonconvex Optimization
Quadric
Nonlinear Optimization
Packing
Charge
Integer
Formulation
Graph in graph theory
Vertex of a graph

Keywords

  • Boolean quadric
  • Facility location
  • Fixed charge
  • Global optimization
  • Mixed-integer nonlinear optimization
  • Monomial
  • Polytope
  • Spatial branch-and-bound
  • Vertex packing
  • Volume

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

Cite this

Algorithmic and modeling insights via volumetric comparison of polyhedral relaxations. / Lee, Jon; Skipper, Daphne E; Speakman, Emily.

In: Mathematical Programming, Vol. 170, No. 1, 01.07.2018, p. 121-140.

Research output: Contribution to journalArticle

Lee, Jon ; Skipper, Daphne E ; Speakman, Emily. / Algorithmic and modeling insights via volumetric comparison of polyhedral relaxations. In: Mathematical Programming. 2018 ; Vol. 170, No. 1. pp. 121-140.
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