Document Zbl 1332.90196

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Program.</a> <a href="/?q=in%3A352650" title="Articles in this Issue">155, No. 1-2 (A), 267-305 (2016)</a>. </div> <div class="abstract">Summary: This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a certain non-differentiable (but convex) component. In order to solve these problems, we propose a randomized stochastic projected gradient (RSPG) algorithm, in which proper mini-batch of samples are taken at each iteration depending on the total budget of stochastic samples allowed. The RSPG algorithm also employs a general distance function to allow taking advantage of the geometry of the feasible region. Complexity of this algorithm is established in a unified setting, which shows nearly optimal complexity of the algorithm for convex stochastic programming. A post-optimization phase is also proposed to significantly reduce the variance of the solutions returned by the algorithm. In addition, based on the RSPG algorithm, a stochastic gradient free algorithm, which only uses the stochastic zeroth-order information, has been also discussed. Some preliminary numerical results are also provided.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6544658">Cited in <strong>104</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C25" title="MSC2020">90C25</a> </td> <td class="space"> Convex programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C06" title="MSC2020">90C06</a> </td> <td class="space"> Large-scale problems in mathematical programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C22" title="MSC2020">90C22</a> </td> <td class="space"> Semidefinite programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A49M37" title="MSC2020">49M37</a> </td> <td class="space"> Numerical methods based on nonlinear programming </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aconstrained+stochastic+programming">constrained stochastic programming</a>; <a href="/?q=ut%3Amini-batch+of+samples">mini-batch of samples</a>; <a href="/?q=ut%3Astochastic+approximation">stochastic approximation</a>; <a href="/?q=ut%3Anonconvex+optimization">nonconvex optimization</a>; <a href="/?q=ut%3Astochastic+programming">stochastic programming</a>; <a href="/?q=ut%3Afirst-order+method">first-order method</a>; <a href="/?q=ut%3Azeroth-order+method">zeroth-order method</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 1332.90196" data-ciurl="/ci/06544658" data-biburl="/bibtex/06544658.bib" data-amsurl="/amsrefs/06544658.bib" data-xmlurl="/xml/06544658.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06544658.pdf" title="Zbl 1332.90196 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/s10107-014-0846-1" aria-label="DOI for “Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization”" title="10.1007/s10107-014-0846-1">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1308.6594"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">Andradóttir, S.: A review of simulation optimization techniques. 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