`constrained_optimization_problem_protocol`

Extends local_optimization_problem_protocol with general equality and inequality constraints. Box constraints continue to be expressed via the inherited position_bounds/1. A problem that defines neither equality_constraints/2 nor inequality_constraints/2 is a plain local_optimization_problem_protocol problem and can still be solved by any constrained_optimization solver.

| Availability: | logtalk_load(constrained_optimization(loader))

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

| Compilation flags: | static

| Extends: | public :ref:`local_optimization_problem_protocol <local_optimization_problem_protocol/0>`

| Remarks:

Equality constraints: g(x) = 0, one component per row of equality_constraints/2.
Inequality constraints: h(x) =< 0, one component per row of inequality_constraints/2. Constraints of the form h(x) >= 0 or a =< h(x) =< b must be restated in this form by the problem (e.g. negate, or split into two rows) before being reported here.
Jacobians: equality_jacobian/2 and inequality_jacobian/2 are required by sqp_active_set(_) and primal_dual_interior_point(_), and by augmented_lagrangian(_,_), quadratic_penalty(_,_), and log_barrier(_,_) when their selected inner solver uses gradients. Solvers that need a Jacobian a problem does not define raise an existence error rather than silently falling back to finite differences.

| 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

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

Public predicates

.. index:: equality_constraints/2 .. _constrained_optimization_problem_protocol/0::equality_constraints/2:

equality_constraints/2 ^^^^^^^^^^^^^^^^^^^^^^^^^^

Computes g(x), the vector of equality constraint values at a point; feasibility requires every component to equal zero. Optional: when not defined, the problem has no equality constraints.

| Compilation flags: | static

| Template: | equality_constraints(Point,Values) | Mode and number of proofs: | equality_constraints(+list(number),-list(number)) - zero_or_one

.. index:: equality_jacobian/2 .. _constrained_optimization_problem_protocol/0::equality_jacobian/2:

equality_jacobian/2 ^^^^^^^^^^^^^^^^^^^^^^^

Computes the Jacobian of equality_constraints/2 at a point, one row per constraint, one column per variable. Optional unless required by the solver in use (see the "Jacobians" remark above).

| Compilation flags: | static

| Template: | equality_jacobian(Point,Jacobian) | Mode and number of proofs: | equality_jacobian(+list(number),-list(list(number))) - zero_or_one

.. index:: inequality_constraints/2 .. _constrained_optimization_problem_protocol/0::inequality_constraints/2:

inequality_constraints/2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Computes h(x), the vector of inequality constraint values at a point; feasibility requires every component to be =< 0. Optional: when not defined, the problem has no general inequality constraints (position_bounds/1 may still apply).

| Compilation flags: | static

| Template: | inequality_constraints(Point,Values) | Mode and number of proofs: | inequality_constraints(+list(number),-list(number)) - zero_or_one

.. index:: inequality_jacobian/2 .. _constrained_optimization_problem_protocol/0::inequality_jacobian/2:

inequality_jacobian/2 ^^^^^^^^^^^^^^^^^^^^^^^^^

Computes the Jacobian of inequality_constraints/2 at a point. Optional unless required by the solver in use (see the "Jacobians" remark above).

| Compilation flags: | static

| Template: | inequality_jacobian(Point,Jacobian) | Mode and number of proofs: | inequality_jacobian(+list(number),-list(list(number))) - zero_or_one

.. index:: inner_progress/6 .. _constrained_optimization_problem_protocol/0::inner_progress/6:

inner_progress/6 ^^^^^^^^^^^^^^^^^^^^

Optional callback reporting progress from an inner solver used by a delegated constrained solver. The stage is outer(N) for an outer iteration or phase1 for a feasibility search. The value and measure are those of the transformed inner subproblem.

| Compilation flags: | static

| Template: | inner_progress(Stage,Iteration,Point,Value,Measure,Evaluations) | Mode and number of proofs: | inner_progress(+term,+non_negative_integer,+list(number),+number,+number,+non_negative_integer) - zero_or_one

Protected predicates

(no local declarations; see entity ancestors if any)

Private predicates

(no local declarations; see entity ancestors if any)

Operators

(none)

.. seealso::

:ref:`local_optimization_problem_protocol <local_optimization_problem_protocol/0>`, :ref:`qp_active_set <qp_active_set/0>`, :ref:`sqp_active_set(Problem) <sqp_active_set/1>`, :ref:`augmented_lagrangian(Problem,InnerSolver) <augmented_lagrangian/2>`, :ref:`quadratic_penalty(Problem,InnerSolver) <quadratic_penalty/2>`, :ref:`log_barrier(Problem,InnerSolver) <log_barrier/2>`, :ref:`primal_dual_interior_point(Problem) <primal_dual_interior_point/1>`