Document Zbl 1508.90071

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Methods Oper. Res.</a> <a href="/?q=in%3A490555" title="Articles in this Issue">96, No. 3, 351-382 (2022)</a>. </div> <div class="abstract">Summary: Based on solving an equivalent parametric equality constrained mini-max problem of the classic logarithmic-barrier subproblem, we present a novel primal-dual interior-point relaxation method for nonlinear programs with general equality and nonnegative constraints. In each iteration, our method approximately solves the KKT system of a parametric equality constrained mini-max subproblem, which avoids the requirement that any primal or dual iterate is an interior-point. The method has some similarities to the warmstarting interior-point methods in relaxing the interior-point requirement and is easily extended for solving problems with general inequality constraints. In particular, it has the potential to circumvent the jamming difficulty that appears with many interior-point methods for nonlinear programs and improve the ill conditioning of existing primal-dual interior-point methods as the barrier parameter is small. A new smoothing approach is introduced to develop our relaxation method and promote convergence of the method. Under suitable conditions, it is proved that our method can be globally convergent and locally quadratically convergent to the KKT point of the original problem. The preliminary numerical results on a well-posed problem for which many interior-point methods fail to find the minimizer and a set of test problems from the CUTEr collection show that our method is efficient.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7628917">Cited in <strong>3</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C26" title="MSC2020">90C26</a> </td> <td class="space"> Nonconvex programming, global optimization </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C30" title="MSC2020">90C30</a> </td> <td class="space"> Nonlinear programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C51" title="MSC2020">90C51</a> </td> <td class="space"> Interior-point methods </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Anonlinear+programming">nonlinear programming</a>; <a href="/?q=ut%3Ainterior-point+relaxation+method">interior-point relaxation method</a>; <a href="/?q=ut%3Asmoothing+method">smoothing method</a>; <a href="/?q=ut%3Alogarithmic-barrier+problem">logarithmic-barrier problem</a>; <a href="/?q=ut%3Amini-max+problem">mini-max problem</a>; <a href="/?q=ut%3Aglobal+and+local+convergence">global and local convergence</a></div> <div class="software"> <h3>Software:</h3><a href="/software/4010">CUTEr</a>; <a href="/software/500">LANCELOT</a>; <a href="/software/4778">ipfilter</a>; <a href="/software/4808">Ipopt</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 1508.90071" data-ciurl="/ci/07628917" data-biburl="/bibtex/07628917.bib" data-amsurl="/amsrefs/07628917.bib" data-xmlurl="/xml/07628917.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07628917.pdf" title="Zbl 1508.90071 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/10.1007/s00186-022-00797-7" aria-label="DOI for “A primal-dual interior-point relaxation method with global and rapidly local convergence for nonlinear programs”" title="10.1007/s00186-022-00797-7">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2007.10803"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">Benson, HY; 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