Document Zbl 1480.65130

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J. Comput. Math.</a> <a href="/?q=in%3A477059" title="Articles in this Issue">97, No. 11, 2233-2258 (2020)</a>. </div> <div class="abstract">Summary: In this paper, we propose two inertial algorithms with new stepsize rule for solving a monotone and Lipschitz variational inequality in a Hilbert space and prove some weak and strong convergence theorems of the proposed inertial algorithms. The algorithms use variable stepsizes which are updated at each iteration by a simple computation without any linesearch. A new stepsize rule presented in the paper has allowed the algorithms to work without the prior knowledge of Lipschitz constant of operator. Finally, we give several numerical results to demonstrate the computational performance of the new algorithms in comparison with other algorithms.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7476505">Cited in <strong>9</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65J15" title="MSC2020">65J15</a> </td> <td class="space"> Numerical solutions to equations with nonlinear operators </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65Y05" title="MSC2020">65Y05</a> </td> <td class="space"> Parallel numerical computation </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47H05" title="MSC2020">47H05</a> </td> <td class="space"> Monotone operators and generalizations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47J25" title="MSC2020">47J25</a> </td> <td class="space"> Iterative procedures involving nonlinear operators </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Avariational+inequality">variational inequality</a>; <a href="/?q=ut%3Amonotone+operator">monotone operator</a>; <a href="/?q=ut%3Aextragradient+method">extragradient method</a>; <a href="/?q=ut%3Asubgradient+extragradient+method">subgradient extragradient method</a>; <a href="/?q=ut%3Aprojection+method">projection 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 1480.65130" data-ciurl="/ci/07476505" data-biburl="/bibtex/07476505.bib" data-amsurl="/amsrefs/07476505.bib" data-xmlurl="/xml/07476505.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07476505.pdf" title="Zbl 1480.65130 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/10.1080/00207160.2019.1686487" aria-label="DOI for “Modified accelerated algorithms for solving variational inequalities”" title="10.1080/00207160.2019.1686487">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">Alvarez, F.; Attouch, H., An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping, Set-Valued Anal., 9, 3-11 (2001) · <a href="/0991.65056" class="nowrap">Zbl 0991.65056</a> · <a href="https://doi.org/10.1023/A:1011253113155" class="nowrap">doi:10.1023/A:1011253113155</a></td> </tr><tr> <td>[2]</td> <td class="space">Attouch, H.; Goudon, X.; Redont, P., The heavy ball with friction. 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