.. _sphx_glr_api_gallery_optimization_newton_quasi_newton:

Newton's method and BFGS
---------------------------

Quasi-Newton BFGS compared with Newton's method and gradient descent on
the Rosenbrock function.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="On the Rosenbrock function from (-1.2, 1.0), BFGS builds an inverse-Hessian approximation from gradients alone. It needs only a few dozen iterations, as few as Newton&#x27;s method with the exact Hessian at every step, while gradient descent needs thousands. Near the minimum its convergence is superlinear: the ratio of successive errors tends to zero.">

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  .. image:: /api/gallery/optimization/newton_quasi_newton/images/thumb/sphx_glr_plot_01_bfgs_quasi_newton_thumb.png
    :alt:

  :doc:`/api/gallery/optimization/newton_quasi_newton/plot_01_bfgs_quasi_newton`

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      <div class="sphx-glr-thumbnail-title">BFGS: Newton-like convergence without second derivatives</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/optimization/newton_quasi_newton/plot_01_bfgs_quasi_newton