.. _vanilla_bayesian_optimization:

Standard Bayesian optimization
==========================================================================================


:Driver: :ref:`BayesianOptimization`


:Download script: :download:`vanilla_bayesian_optimization.py`


The target of the study is to run a standard Bayesian optimization of a scalar function. As an example, the 2D `Rastrigin function <https://en.wikipedia.org/wiki/Rastrigin_function>`_ on a circular domain is minimized,

.. math::

   &\text{min.}\,& f(x_1,x_2) = 2\cdot10 + \sum_{i=1,2} \left(x_i^2 - 10\cos(2\pi x_i)\right)
   
   &\text{s.t.}\,& \sqrt{x_1^2 + x_2^2} \leq 1.5.



.. literalinclude:: ./vanilla_bayesian_optimization.py
   :language: python
   :linenos: