.. 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: | Â :ref:`local_optimization_problem_protocol/0::gradient/2` Â :ref:`local_optimization_problem_protocol/0::hessian/2` Â :ref:`local_optimization_problem_protocol/0::initial_point/1` Â :ref:`local_optimization_problem_protocol/0::objective/2` Â :ref:`local_optimization_problem_protocol/0::position_bounds/1` Â :ref:`local_optimization_problem_protocol/0::progress/5` Â :ref:`local_optimization_problem_protocol/0::stop_condition/3` Â

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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)