.. index:: single: phase1_sub_problem(Problem,StartPoint)
.. _phase1_sub_problem/2:

.. rst-class:: right

**object**

``phase1_sub_problem(Problem,StartPoint)``
==========================================

* ``Problem`` - The original constrained problem.
* ``StartPoint`` - The point log_barrier(_,_) was actually given (Problem's own initial_point/1); phase 1 starts its search from here.


Internal phase-1 feasibility subproblem for log_barrier(_,_): minimizes sum_j max(0, h_j(x) + margin)^2 (margin = 1.0e-6), an ordinary smooth, everywhere-defined unconstrained objective, so a minimizer that reaches (near) zero gives a point with every h_j(x) < -margin, comfortably inside the barrier's domain rather than exactly on its boundary. Instantiated once, when initial_point/1 is not already strictly feasible; not meant to be used directly. See log_barrier(_,_)'s "ensure_strictly_feasible/3" for how the result is validated and how this heuristic falls back to raising domain_error/2 when it does not succeed.

| **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>`
| **Uses:**
|    :ref:`linear_algebra <linear_algebra/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
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(no local declarations; see entity ancestors if any)

Private predicates
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(no local declarations; see entity ancestors if any)

Operators
---------

(none)