.. _method-polynomial_chaos-expansion_order-collocation_ratio-basis_pursuit_denoising:

"""""""""""""""""""""""
basis_pursuit_denoising
"""""""""""""""""""""""


Compute the coefficients of a polynomial expansion by solving the Basis Pursuit Denoising :math:`\ell_1` -minimization problem using second order cone optimization.


.. toctree::
   :hidden:
   :maxdepth: 1

   method-polynomial_chaos-expansion_order-collocation_ratio-basis_pursuit_denoising-noise_tolerance


**Specification**

- *Alias:* bpdn 

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+---------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword      | Dakota Keyword Description                    |
|                         | Group              |                     |                                               |
+=========================+====================+=====================+===============================================+
| Optional                                     | `noise_tolerance`__ | The noise tolerance used when performing      |
|                                              |                     | cross validation in the presence of noise or  |
|                                              |                     | truncation errors.                            |
+----------------------------------------------+---------------------+-----------------------------------------------+

.. __: method-polynomial_chaos-expansion_order-collocation_ratio-basis_pursuit_denoising-noise_tolerance.html



**Description**


Compute the coefficients of a polynomial expansion by solving the Basis Pursuit Denoising :math:`\ell_1` -minimization problem using second order cone optimization.