<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>136</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2017-03-19</completedDate>
    <publishedDate>2017-03-19</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Deciding Robust Feasibility and Infeasibility Using a Set Containment Approach: An Application to Stationary Passive Gas Network Operations</title>
    <abstract language="eng">In this paper we study feasibility and infeasibility of nonlinear two-stage&#13;
fully adjustable robust feasibility problems with an empty first stage. This&#13;
is equivalent to deciding set containment of a projection of the feasible&#13;
region and the uncertainty set. For answering this question, two very general&#13;
approaches using methods from polynomial optimization are presented --- one&#13;
for showing feasibility and one for showing infeasibility. The developed&#13;
methods are approximated through sum of squares polynomials and solved using&#13;
semidefinite programs.&#13;
&#13;
Deciding robust feasibility and infeasibility is important for gas network&#13;
operations, which is a \nonconvex quadratic problem with absolute values&#13;
functions. Concerning the gas network problem, different topologies are&#13;
considered. It is shown that a tree structured network can be decided exactly&#13;
using linear programming. Furthermore, a method is presented to reduce a tree&#13;
network with one additional arc to a single cycle network. In this case,&#13;
removing the absolute values and solving the problem can be decided with&#13;
linearly many polynomial optimization problems.&#13;
&#13;
Lastly, the effectivity of the methods is tested on a variety of small cyclic&#13;
networks. For instances where robust feasibility or infeasibility can be&#13;
decided, level~2 or level~3 of the Lasserre relaxation hierarchy is typically&#13;
sufficient.</abstract>
    <enrichment key="review.accepted_by">2</enrichment>
    <author>Denis Aßmann</author>
    <author>Frauke Liers</author>
    <author>Michael Stingl</author>
    <author>Juan Vera</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>robust optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polynomial optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stationary gas transport</value>
    </subject>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="subprojects" number="">B06</collection>
    <collection role="institutes" number="">Tilburg University</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/136/poly-set-containment-gas.pdf</file>
  </doc>
</export-example>
