.. index:: single: augmented_lagrangian(Problem,InnerSolver)
.. _augmented_lagrangian/2:

.. rst-class:: right

**object**

``augmented_lagrangian(Problem,InnerSolver)``
=============================================

* ``Problem`` - Problem object implementing ``constrained_optimization_problem_protocol``.
* ``InnerSolver`` - Atom naming a local_optimization solver class taking a single problem parameter, e.g. ``bfgs`` or ``lbfgs``. Constructed dynamically each outer iteration as ``InnerSolver(SubProblem)``.


Augmented Lagrangian method for problems with general equality and inequality constraints, delegating each penalized subproblem to an existing local optimization solver.

| **Availability:** 
|    ``logtalk_load(constrained_optimization(loader))``

| **Author:** Paulo Moura
| **Version:** 1:0:0
| **Date:** 2026-09-03

| **Compilation flags:**
|    ``static, context_switching_calls``


| **Imports:**
|    ``public`` :ref:`constrained_optimization_solver <constrained_optimization_solver/0>`
|    ``public`` :ref:`local_optimization_solver(Problem) <local_optimization_solver/1>`
| **Uses:**
|    :ref:`linear_algebra <linear_algebra/0>`
|    :ref:`list <list/0>`

| **Remarks:**
|    (none)

| **Inherited public predicates:**
|     :ref:`options_protocol/0::check_option/1`  :ref:`options_protocol/0::check_options/1`  :ref:`options_protocol/0::default_option/1`  :ref:`options_protocol/0::default_options/1`  :ref:`options_protocol/0::option/2`  :ref:`options_protocol/0::option/3`  :ref:`local_optimization_solver/1::run/2`  :ref:`local_optimization_solver/1::run/3`  :ref:`local_optimization_solver/1::run/4`  :ref:`options_protocol/0::valid_option/1`  :ref:`options_protocol/0::valid_options/1`  

.. contents::
   :local:
   :backlinks: top

Public predicates
-----------------

(no local declarations; see entity ancestors if any)

Protected predicates
--------------------

(no local declarations; see entity ancestors if any)

Private predicates
------------------

(no local declarations; see entity ancestors if any)

Operators
---------

(none)

.. seealso::

   :ref:`constrained_optimization_problem_protocol <constrained_optimization_problem_protocol/0>`, :ref:`sqp_active_set(Problem) <sqp_active_set/1>`, :ref:`local_optimization_solver(Problem) <local_optimization_solver/1>`, :ref:`bfgs(Problem) <bfgs/1>`, :ref:`lbfgs(Problem) <lbfgs/1>`