Document Zbl 1262.90170

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Optim. Theory Appl.</a> <a href="/?q=in%3A301302" title="Articles in this Issue">153, No. 3, 733-757 (2012)</a>. </div> <div class="abstract">Making use of the three-term conjugate gradient methods by <span class="zbmathjax-textit">Y. Narushima, H. Yabe</span> and <span class="zbmathjax-textit">J. A. Ford</span> [SIAM J. Optim. 21, No. 1, 212–230 (2011; <a href="/1250.90087">Zbl 1250.90087</a>)], the authors propose three-term conjugate gradient methods based on secant conditions for unconstrained optimization problems and prove the global convergence of the methods. Special-purpose three-term conjugate gradient methods based on structured secant conditions are also given together with applying them to nonlinear least squares problems and some numerical experiments.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A10357">Do Van Luu (Hanoi)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A6062505">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A6062505">Cited in <strong>49</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A90C53" title="MSC2020">90C53</a> </td> <td class="space"> Methods of quasi-Newton type </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Athree-term+conjugate+gradient+methods">three-term conjugate gradient methods</a>; <a href="/?q=ut%3Asecant+conditions">secant conditions</a>; <a href="/?q=ut%3Aglobal+convergence">global convergence</a>; <a href="/?q=ut%3Aunconstrained+optimization+problems">unconstrained optimization problems</a>; <a href="/?q=ut%3Adescent+search+directions">descent search directions</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1250.90087">Zbl 1250.90087</a></div> <div class="software"> <h3>Software:</h3><a href="/software/4813">CG_DESCENT</a>; <a href="/software/4010">CUTEr</a>; <a href="/software/5310">minpack</a>; <a href="/software/14681">CUTE</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 1262.90170" data-ciurl="/ci/06062505" data-biburl="/bibtex/06062505.bib" data-amsurl="/amsrefs/06062505.bib" data-xmlurl="/xml/06062505.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06062505.pdf" title="Zbl 1262.90170 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/s10957-011-9960-x" aria-label="DOI for “Globally convergent three-term conjugate gradient methods that use secant conditions and generate descent search directions for unconstrained optimization”" title="10.1007/s10957-011-9960-x">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Fletcher, R., Reeves, C.M.: Function minimization by conjugate gradients. 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