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lines 6-63 of file: example/user/warm_start.cpp
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{xrst_begin warm_start.cpp}

Warm Starting Optimization: Example and Test
############################################

Model
*****

.. math::

   \B{p}( z_i | \theta ) \sim \B{N} ( \theta_i , 1 )

with no prior on :math:`\theta`.
The corresponding fixed likelihood
:ref:`g(theta)<theory@Fixed Likelihood, g(theta)>`
is

.. math::

   g( \theta ) = \frac{1}{2} \sum_{i} \left[
      \log ( 2 \pi ) + ( z_i - \theta_i )^2
   \right]

We do not include the constant term :math:`\log( 2 \pi )`
in the fixed likelihood.
The optimal solution (with no constraints) is

.. math::

   \hat{\theta}_i = z_i

Bounds
******
We add lower and upper bounds that are not active at the optimal solution.
To be specific

.. math::

   0 \leq \theta_i \leq z_i + 1

Maximum Iterations
******************
We use 5 for the maximum number of iterations so that the optimization
problem does not solve on the first try.
A warm start is used and the problem does solve within the limit
of another 5 iterations.

Optimizer Trace
***************
This example uses the optimizer trace information; see
:ref:`fixed_solution@trace_vec` .

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{xrst_end warm_start.cpp}