protocol

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 local_optimization_problem_protocol

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:

 gradient/2  hessian/2  initial_point/1  objective/2  position_bounds/1  progress/5  stop_condition/3

Public predicates

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

---

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

---

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

---

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

---

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)

See also

local_optimization_problem_protocol, qp_active_set, sqp_active_set(Problem), augmented_lagrangian(Problem,InnerSolver), quadratic_penalty(Problem,InnerSolver), log_barrier(Problem,InnerSolver), primal_dual_interior_point(Problem)