Preprint Open Access

Approximations of Countably Infinite Linear Programs over Bounded Measure Spaces

Kuntz, Juan; Thomas, Philipp; Stan, Guy-Bart; Barahona, Mauricio


DataCite XML Export

<?xml version='1.0' encoding='utf-8'?>
<resource xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://datacite.org/schema/kernel-4" xsi:schemaLocation="http://datacite.org/schema/kernel-4 http://schema.datacite.org/meta/kernel-4.1/metadata.xsd">
  <identifier identifierType="URL">https://zenodo.org/record/4836001</identifier>
  <creators>
    <creator>
      <creatorName>Kuntz, Juan</creatorName>
      <givenName>Juan</givenName>
      <familyName>Kuntz</familyName>
      <nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0002-5855-6074</nameIdentifier>
      <affiliation>Department of Mathematics and Department of Bioengineering, Imperial College London, London SW7 2AZ, United Kingdom.</affiliation>
    </creator>
    <creator>
      <creatorName>Thomas, Philipp</creatorName>
      <givenName>Philipp</givenName>
      <familyName>Thomas</familyName>
      <nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0003-4919-8452</nameIdentifier>
      <affiliation>Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom</affiliation>
    </creator>
    <creator>
      <creatorName>Stan, Guy-Bart</creatorName>
      <givenName>Guy-Bart</givenName>
      <familyName>Stan</familyName>
      <nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0002-5560-902X</nameIdentifier>
      <affiliation>Department of Bioengineering, Imperial College London, London SW7 2AZ, United Kingdom</affiliation>
    </creator>
    <creator>
      <creatorName>Barahona, Mauricio</creatorName>
      <givenName>Mauricio</givenName>
      <familyName>Barahona</familyName>
      <nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0002-1089-5675</nameIdentifier>
      <affiliation>Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Approximations of Countably Infinite Linear Programs over Bounded Measure Spaces</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2021</publicationYear>
  <dates>
    <date dateType="Issued">2021-02-18</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Preprint</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/4836001</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1137/19M1268847</relatedIdentifier>
    <relatedIdentifier relatedIdentifierType="URL" relationType="IsPartOf">https://zenodo.org/communities/cosy-bio</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="https://creativecommons.org/licenses/by/4.0/legalcode">Creative Commons Attribution 4.0 International</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&lt;p&gt;&lt;strong&gt;Abstract&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;We study a class of countably infinite linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined spaces of measures. The optimal value, optimal points, and minimal points of these CILPs can be approximated by solving finite-dimensional linear programs. We show how to construct finite-dimensional programs that lead to approximations with easy-to-evaluate error bounds, and we prove that the errors converge to zero as the size of the finite-dimensional programs approaches that of the original problem. We discuss the use of our methods in the computation of the stationary distributions, occupation measures, and exit distributions of Markov chains.&lt;br&gt;
&lt;br&gt;
&lt;br&gt;
Read More:&amp;nbsp;&lt;a href="https://epubs.siam.org/doi/10.1137/19M1268847"&gt;https://epubs.siam.org/doi/10.1137/19M1268847&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;&amp;nbsp;&lt;/p&gt;

&lt;p&gt;&amp;nbsp;&lt;/p&gt;

&lt;p&gt;&amp;nbsp;&lt;/p&gt;</description>
  </descriptions>
  <fundingReferences>
    <fundingReference>
      <funderName>European Commission</funderName>
      <funderIdentifier funderIdentifierType="Crossref Funder ID">10.13039/501100000780</funderIdentifier>
      <awardNumber awardURI="info:eu-repo/grantAgreement/EC/H2020/766840/">766840</awardNumber>
      <awardTitle>Control Engineering of Biological Systems for Reliable Synthetic Biology Applications</awardTitle>
    </fundingReference>
  </fundingReferences>
</resource>
2
3
views
downloads
Views 2
Downloads 3
Data volume 820.3 kB
Unique views 2
Unique downloads 3

Share

Cite as