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a target function value <small>\(10^{-2}\)</small>, it suffices to replace <code>pdfo(chrosen, x0)</code> in the above example by
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</p>
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<pre class="shadow-lg rounded"><code class="displayed hljs">pdfo(chrosen, x0, method='lincoa', options={'maxfev': 50, 'ftarget': 1e-2})</code></pre>
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<header class="docs-header">
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<h1>References <span class="docs-time d-none d-md-flex">Last update: August 23, 2021</span></h1>
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<h1>Citation <span class="docs-time d-none d-md-flex">Last update: June 15, 2023</span></h1>
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<section class="docs-intro">
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<p>
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If you use PDFO, please cite the following paper. Note that PDFO
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contains improvements and bug fixes that do not exist in Powell's
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original code. See Subsections 4.3&ndash;4.5 of the paper below for details.
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</p>
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<p>
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T. M. Ragonneau and Z. Zhang, <a class="theme-link" href="https://arxiv.org/pdf/2302.13246.pdf" target="_blank">PDFO: a cross-platform package for
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Powell's derivative-free optimization solvers</a>, <a class="theme-link" href="https://arxiv.org/abs/2302.13246" target="_blank">arXiv:2302.13246</a>, 2023.
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</p>
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<pre class="shadow-lg rounded"><code class="displayed hljs">@misc{Ragonneau_Zhang_2023,
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title = {{PDFO}: a cross-platform package for {P}owell's derivative-free optimization solvers},
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author = {Ragonneau, T. M. and Zhang, Z.},
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howpublished = {arXiv:2302.13246},
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year = 2023,
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}</code></pre>
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<p>
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In addition, references for Powell's methods are as follows.
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</p>
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<p>
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<a class="theme-link" href="https://link.springer.com/chapter/10.1007/978-94-015-8330-5_4" target="_blank">[1]</a>
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M. J. D. Powell, A direct search optimization method that models the objective and constraint functions by linear interpolation, In Advances in Optimization and Numerical Analysis, eds. S. Gomez and J. P. Hennart, pages 51--67, Springer Verlag, Dordrecht, Netherlands, 1994
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M. J. D. Powell, A direct search optimization method that models the objective and constraint functions by linear interpolation, In Advances in Optimization and Numerical Analysis, eds. S. Gomez and J. P. Hennart, pages 51&ndash;67, Springer Verlag, Dordrecht, Netherlands, 1994
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</p>
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<p>
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<a class="theme-link" href="http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2000_14.ps.gz" target="_blank">[2]</a>
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M. J. D. Powell, UOBYQA: unconstrained optimization by quadratic approximation, <i>Math. Program.</i>, 92(B):555--582, 2002
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M. J. D. Powell, UOBYQA: unconstrained optimization by quadratic approximation, <i>Math. Program.</i>, 92(B):555&ndash;582, 2002
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</p>
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<p>
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<a class="theme-link" href="http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2002_08.ps.gz" target="_blank">[3]</a>
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M. J. D. Powell, Least Frobenius norm updating of quadratic models that satisfy interpolation conditions. <i>Math. Program.</i>, 100:183--215, 2004
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M. J. D. Powell, Least Frobenius norm updating of quadratic models that satisfy interpolation conditions. <i>Math. Program.</i>, 100:183&ndash;215, 2004
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</p>
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<p>
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<a class="theme-link" href="http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2003_03.ps.gz" target="_blank">[4]</a>
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M. J. D. Powell, On the use of quadratic models in unconstrained minimization without derivatives, <i>Optim. Methods Softw.</i>, 19:399--411, 2004
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M. J. D. Powell, On the use of quadratic models in unconstrained minimization without derivatives, <i>Optim. Methods Softw.</i>, 19:399&ndash;411, 2004
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</p>
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<p>
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<a class="theme-link" href="http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2004_01.pdf" target="_blank">[5]</a>
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M. J. D. Powell, On updating the inverse of a KKT matrix, in <i>Numerical Linear Algebra and Optimization</i>, ed. Ya-xiang Yuan, Science Press (Beijing), pp. 56--78, 2004
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M. J. D. Powell, On updating the inverse of a KKT matrix, in <i>Numerical Linear Algebra and Optimization</i>, ed. Ya-xiang Yuan, Science Press (Beijing), pp. 56&ndash;78, 2004
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</p>
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<p>
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<a class="theme-link" href="http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2004_08.pdf" target="_blank">[6]</a>
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M. J. D. Powell, The NEWUOA software for unconstrained optimization without derivatives, In <i>Large-Scale Nonlinear Optimization</i>, eds. G. Di Pillo and M. Roma, pages 255--297, Springer, New York, US, 2006
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M. J. D. Powell, The NEWUOA software for unconstrained optimization without derivatives, In <i>Large-Scale Nonlinear Optimization</i>, eds. G. Di Pillo and M. Roma, pages 255&ndash;297, Springer, New York, US, 2006
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</p>
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<p>
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<a class="theme-link" href="http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2007_03.pdf" target="_blank">[7]</a>
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M. J. D. Powell, A view of algorithms for optimization without derivatives, Technical Report DAMTP 2007/NA63, Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, UK, 2007
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</p>
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<p>
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<a class="theme-link" href="http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2007_05.pdf" target="_blank">[8]</a>
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M. J. D. Powell, Developments of NEWUOA for minimization without derivatives, <i>IMA J. Numer. Anal.</i>, 28:649--664, 2008
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M. J. D. Powell, Developments of NEWUOA for minimization without derivatives, <i>IMA J. Numer. Anal.</i>, 28:649&ndash;664, 2008
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</p>
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<p>
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<a class="theme-link" href="http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf" target="_blank">[9]</a>
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M. J. D. Powell, The BOBYQA algorithm for bound constrained optimization without derivatives, Technical Report DAMTP 2009/NA06, Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, UK, 2009
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</p>
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<a class="theme-link" href="http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2014_02.pdf" target="_blank">[10]</a>
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M. J. D. Powell, On fast trust region methods for quadratic models with linear constraints, <i>Math. Program. Comput.</i>, 7:237--267, 2015
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M. J. D. Powell, On fast trust region methods for quadratic models with linear constraints, <i>Math. Program. Comput.</i>, 7:237&ndash;267, 2015
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</p>
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<p>
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<a class="theme-link" href="https://tomragonneau.com/documents/thesis.pdf" target="_blank">[11]</a>
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T. M. Ragonneau. <i>Model-Based Derivative-Free Optimization Methods and Software</i>, Chapter 3. PhD thesis, The Hong Kong Polytechnic University, Hong Kong SAR, China, 2022.
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</p>
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<p>
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<a class="theme-link" href="http://www.libprima.net" target="_blank">[12]</a>
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Z. Zhang, PRIMA: Reference Implementation for Powell's Methods
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with Modernization and Amelioration, available at
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<a class="theme-link" href="http://www.libprima.net" target="_blank">http://www.libprima.net</a>, 2023.
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<h2>Remarks</h2>

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