.. index:: single: sub_problem(Problem,OuterIteration,StartPoint,EqLambda,IneqLambda,Rho,Sign)
.. _sub_problem/7:

.. rst-class:: right

**object**

``sub_problem(Problem,OuterIteration,StartPoint,EqLambda,IneqLambda,Rho,Sign)``
===============================================================================

* ``Problem`` - The original constrained problem.
* ``OuterIteration`` - One-based outer iteration number.
* ``StartPoint`` - Point the inner solve should start from (the current outer iterate).
* ``EqLambda`` - Current equality-constraint multiplier estimates (possibly []).
* ``IneqLambda`` - Current inequality-constraint multiplier estimates (possibly []).
* ``Rho`` - Current penalty parameter.
* ``Sign`` - 1.0 to minimize the original objective, -1.0 to maximize it.


Internal augmented-Lagrangian penalized subproblem: objective(x) = Sign*f(x) + penalty(x), where penalty adds the Hestenes-Powell term for each equality constraint and the smooth Rockafellar/Bertsekas term for each inequality constraint at the current multiplier estimates EqLambda/IneqLambda and penalty parameter Rho. Instantiated fresh by augmented_lagrangian(_,_) every outer iteration, starting from StartPoint (the previous outer iterate, not Problem's own initial_point/1, so each inner solve warm-starts from where the outer loop left off); not meant to be used directly.

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

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

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


| **Implements:**
|    ``public`` :ref:`local_optimization_problem_protocol <local_optimization_problem_protocol/0>`
| **Imports:**
|    ``public`` :ref:`constrained_optimization_solver <constrained_optimization_solver/0>`
| **Uses:**
|    :ref:`linear_algebra <linear_algebra/0>`
|    :ref:`list <list/0>`

| **Remarks:**
|    (none)

| **Inherited public predicates:**
|     :ref:`local_optimization_problem_protocol/0::gradient/2`  :ref:`local_optimization_problem_protocol/0::hessian/2`  :ref:`local_optimization_problem_protocol/0::initial_point/1`  :ref:`local_optimization_problem_protocol/0::objective/2`  :ref:`local_optimization_problem_protocol/0::position_bounds/1`  :ref:`local_optimization_problem_protocol/0::progress/5`  :ref:`local_optimization_problem_protocol/0::stop_condition/3`  

.. 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)