Document Zbl 1496.65080

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Algorithms</a> <a href="/?q=in%3A485263" title="Articles in this Issue">91, No. 1, 145-160 (2022)</a>. </div> <div class="abstract">Summary: At present, many conjugate gradient methods with global convergence have been proposed in unconstrained optimization, such as MPRP algorithm proposed by <span class="zbmathjax-textit">L. Zhang</span> et al. [IMA J. Numer. Anal. 26, No. 4, 629–640 (2006; <a href="/1106.65056">Zbl 1106.65056</a>)]. Unfortunately, almost all of these methods require gradient Lipschitz continuity condition. As far as we know, how do the current conjugate gradient methods deal with gradient non-Lipschitz continuity problems is basically blank. For gradient non-Lipschitz continuity problems, Algorithm 1 and Algorithm 2 are proposed in this paper based on MPRP algorithm. The proposed algorithms have the following characteristics: (i) Algorithm 1 retains sufficient descent property independent of line search technology in MPRP algorithm; (ii) for nonconvex and gradient non-Lipschitz continuous functions, the global convergence of Algorithm 1 is obtained in combination with the trust region property and the weak Wolfe-Powell line search technique; (iii) based on Algorithm 1, Algorithm 2 is further improved which global convergence can be obtained independently of line search technique; (iv) according to numerical experiments, the proposed algorithms perform competitively with other similar algorithms.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7570463">Cited in <strong>6</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65K05" title="MSC2020">65K05</a> </td> <td class="space"> Numerical mathematical programming methods </td> </tr><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%3A90C52" title="MSC2020">90C52</a> </td> <td class="space"> Methods of reduced gradient type </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aconjugate+gradient">conjugate gradient</a>; <a href="/?q=ut%3Anonconvex+functions">nonconvex functions</a>; <a href="/?q=ut%3Asufficient+descent+property">sufficient descent property</a>; <a href="/?q=ut%3Aglobal+convergence">global convergence</a>; <a href="/?q=ut%3Agradient+Lipschitz+continuity+condition">gradient Lipschitz continuity condition</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1106.65056">Zbl 1106.65056</a></div> <div class="software"> <h3>Software:</h3><a href="/software/4813">CG_DESCENT</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 1496.65080" data-ciurl="/ci/07570463" data-biburl="/bibtex/07570463.bib" data-amsurl="/amsrefs/07570463.bib" data-xmlurl="/xml/07570463.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07570463.pdf" title="Zbl 1496.65080 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/s11075-022-01257-3" aria-label="DOI for “Adaptive three-term PRP algorithms without gradient Lipschitz continuity condition for nonconvex functions”" title="10.1007/s11075-022-01257-3">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">Al-Baali, M., Descent property and global convergence of the Fletcher-Reeves method with inexact line search[J], IMA J. 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