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Extreme points of a ball about a measure with finite support

Owhadi, Houman and Scovel, Clint (2017) Extreme points of a ball about a measure with finite support. Communications in Mathematical Sciences, 15 (1). pp. 77-96. ISSN 1539-6746. https://resolver.caltech.edu/CaltechAUTHORS:20160223-151629237

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Abstract

We show that, for the space of Borel probability measures on a Borel subset of a Polish metric space, the extreme points of the Prokhorov, Monge–Wasserstein and Kantorovich metric balls about a measure whose support has at most n points, consist of measures whose supports have at most n+2 points. Moreover, we use the Strassen and Kantorovich–Rubinstein duality theorems to develop representations of supersets of the extreme points based on linear programming, and then develop these representations towards the goal of their efficient computation.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.4310/CMS.2017.v15.n1.a4DOIArticle
http://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0015/0001/a004/PublisherArticle
http://arxiv.org/abs/1504.06745arXivDiscussion Paper
ORCID:
AuthorORCID
Owhadi, Houman0000-0002-5677-1600
Scovel, Clint0000-0001-7757-3411
Additional Information:© 2017 International Press of Boston, Inc. The authors gratefully acknowledge this work supported by the Air Force Office of Scientific Research under Award Number FA9550-12-1-0389 (Scientific Computation of Optimal Statistical Estimators).
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-12-1-0389
Subject Keywords:extreme points, Prokhorov, Kantorovich, Monge–Wasserstein, Strassen, Kantorovich–Rubinstein, optimization, ambiguity
Issue or Number:1
Classification Code:2010 Mathematics Subject Classification: 52A05, 60D05
Record Number:CaltechAUTHORS:20160223-151629237
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160223-151629237
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64687
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:24 Feb 2016 00:17
Last Modified:03 Oct 2019 09:40

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