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{xrst_begin trace_fixed_table}
{xrst_spell
  biegler
  iter
  wachter
}

The Fixed Effects Optimization Trace Table
##########################################

Discussion
**********
The trace_fixed table contains the ipopt trace information
for optimizing the fixed effects during the most recent
:ref:`fit fixed<fit_command@variables@fixed>` or
:ref:`fit both<fit_command@variables@both>` command.
Each row of this table corresponds to one iteration of the
fixed effects optimization.

trace_fixed_id
**************
This column has type ``integer`` and
is the primary key for the data table.
Its initial value is zero, and it increments by one for each row.
Note that all the variables and constraints have been re-scaled by
dismod_at and cppad_mixed before ipopt even sees the problem.

iter
****
This column has type ``integer`` and
is the current iteration count (which is equal to *trace_fixed_id* ).
This includes regular iterations and iterations during the restoration phase.

obj_value
*********
This column has type ``real`` and
is the objective value at the current point.

inf_pr
******
This column has type ``real`` and
is the constraint violation at the current point.
This quantity is the infinity-norm (max) of the constraint
violation for :math:`g(x)` in the Ipopt documentation.
During the restoration phase, this value remains the constraint
violation of the original problem at the current point.
The option ``inf_pr_output`` can be used to switch to the printing of
a different quantity.

inf_du
******
This column has type ``real`` and
is the dual infeasibility at the current point.
This quantity measure the infinity-norm (max) of the
internal dual infeasibility, i.e, the derivative of the lagrangian
with respect to the primal variables

.. math::

    \nabla f(x) \nabla c(x) \lambda - z

where :math:`z` are the lagrange multipliers for the box constraints and
:math:`c(x)` are the nonlinear equality constraints
(inequality constraints are reformulated using slack variables
and problem scaling).
During the restoration phase,
this is the value of the dual infeasibility for the restoration phase problem.

mu
**
This column has type ``real`` and
is the value of the barrier parameter :math:`\mu`.

d_norm
******
This column has type ``real`` and
is the infinity norm (max) of the primal step
(for the original variables :math:`x` and the internal slack
variables :math:`s`).
During the restoration phase,
this value includes the values of additional variables that
capture the violation in :math:`c(x) = 0`.

regularization_size
*******************
This column has type ``real`` and
is the value of the regularization term for the Hessian
of the Lagrangian in the augmented system.

alpha_du
********
This column has type ``real`` and
is the step size for the dual variables for the box constraints in the
equality constrained formulation; i.e., :math:`z`.

alpha_pr
********
This column has type ``real`` and
is the step size for the primal variables
:math:`x` and :math:`\lambda` in the equality constrained formulation.
The number is usually followed by a character for additional diagnostic
information regarding the step acceptance criterion.

ls_trials
*********
This column has type ``integer`` and
is the number of backtracking line search steps
(does not include second-order correction steps).

restoration
***********
This column has type ``integer`` is zero or one.
If it is one (zero), this is a restoration iteration
(is not a restoration iteration).

Reference
*********
A. Wachter and L. T. Biegler.,
On the implementation of a primal-dual interior point
filter line search algorithm for large-scale nonlinear programming.
Mathematical Programming, 106(1):25-57, 2006.

{xrst_end trace_fixed_table}