Document Zbl 1455.90121

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Res.</a> <a href="/?q=in%3A453942" title="Articles in this Issue">66, No. 3, 849-869 (2018)</a>. </div> <div class="abstract">Summary: Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the corresponding approximation error can be substantial. In this paper we show that two-stage robust and distributionally robust linear programs can often be reformulated exactly as conic programs that scale polynomially with the problem dimensions. Specifically, when the ambiguity set constitutes a 2-Wasserstein ball centered at a discrete distribution, the distributionally robust linear program is equivalent to a copositive program (if the problem has complete recourse) or can be approximated arbitrarily closely by a sequence of copositive programs (if the problem has sufficiently expensive recourse). These results directly extend to the classical robust setting and motivate strong tractable approximations of two-stage problems based on semidefinite approximations of the copositive cone. We also demonstrate that the two-stage distributionally robust optimization problem is equivalent to a tractable linear program when the ambiguity set constitutes a 1-Wasserstein ball centered at a discrete distribution and there are no support constraints.<br class="zbmathjax-paragraph">The online appendix is available at <a href="https://doi.org/10.1287/opre.2017.1698">https://doi.org/10.1287/opre.2017.1698</a>.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7258954">Cited in <strong>56</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C17" title="MSC2020">90C17</a> </td> <td class="space"> Robustness in mathematical programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C30" title="MSC2020">90C30</a> </td> <td class="space"> Nonlinear programming </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Atwo-stage+decision+problems">two-stage decision problems</a>; <a href="/?q=ut%3Adistributionally+robust+optimization">distributionally robust optimization</a>; <a href="/?q=ut%3Acopositive+programming">copositive programming</a></div> <div class="software"> <h3>Software:</h3><a href="/software/11049">ElemStatLearn</a>; <a href="/software/4733">ROME</a>; <a href="/software/4595">YALMIP</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1455.90121" data-ciurl="/ci/07258954" data-biburl="/bibtex/07258954.bib" data-amsurl="/amsrefs/07258954.bib" data-xmlurl="/xml/07258954.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07258954.pdf" title="Zbl 1455.90121 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1287/opre.2017.1698" aria-label="DOI for “Conic programming reformulations of two-stage distributionally robust linear programs over Wasserstein balls”" title="10.1287/opre.2017.1698">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1609.07505"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ardestani-Jaafari A, Delage E (2016) Linearized robust counterparts of two-stage robust optimization problems with applications in operations management. 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