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Pointed Closed Convex Sets are the Intersection of All Rational Supporting Closed Halfspaces

Marcel de Carli Silva(marcel.csilva***at***gmail.com)
Levent Tunšel(ltuncel***at***uwaterloo.ca)

Abstract: We prove that every pointed closed convex set in $\mathbb{R}^n$ is the intersection of all the rational closed halfspaces that contain it. This generalizes a previous result by the authors for compact convex sets.

Keywords: separation theorem, convex analysis

Category 1: Convex and Nonsmooth Optimization

Category 2: Integer Programming

Citation: arXiv:1802.03296. February 2018

Download: [PDF]

Entry Submitted: 02/13/2018
Entry Accepted: 02/13/2018
Entry Last Modified: 02/13/2018

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