<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>284</id>
    <completedYear>2019</completedYear>
    <publishedYear/>
    <thesisYearAccepted>2022</thesisYearAccepted>
    <language>eng</language>
    <pageFirst>417</pageFirst>
    <pageLast>441</pageLast>
    <pageNumber>25</pageNumber>
    <edition/>
    <issue>29(1)</issue>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2019-10-10</completedDate>
    <publishedDate>2019-10-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Γ-Robust Linear Complementarity Problems with Ellipsoidal Uncertainty Sets</title>
    <abstract language="eng">We study uncertain linear complementarity problems (LCPs), i.e., problems in which the LCP vector q or the LCP matrix M may contain uncertain parameters. To this end, we use the concept of Γ-robust optimization applied to the gap function formulation of the LCP. Thus, this work builds upon [16]. There, we studied Γ-robustified LCPs for l1- and box-uncertainty sets, whereas we now focus on ellipsoidal uncertainty set. For uncertainty in q or M, we derive conditions for the tractability of the robust counterparts. For these counterparts, we also give conditions for the existence and uniqueness of their solutions. Finally, a case study for the uncertain traffic equilibrium problem is considered, which illustrates the effects of the values of Γ on the feasibility and quality of the respective robustified solutions.</abstract>
    <parentTitle language="deu">International Transactions in Operational Research</parentTitle>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Vanessa Krebs</author>
    <author>Michael Müller</author>
    <author>Martin Schmidt</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Robust optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Linear complementarity problems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Ellipsoidal uncertainty sets</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Traffic equilibrium problems</value>
    </subject>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="subprojects" number="">A05</collection>
    <collection role="subprojects" number="">B08</collection>
    <collection role="institutes" number="">Universität Trier</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/284/gamma-robust-lcps-w-ellipsoids_preprint.pdf</file>
  </doc>
</export-example>
