`trust_region_newton_cg(Problem)`

Problem - Problem object implementing local_optimization_problem_protocol and defining gradient/2 and hessian/2. Trust-region Newton-CG local optimizer (Steihaug-CG for the subproblem). Requires the problem to define gradient/2 and hessian/2. Supports optional box constraints via projection, minimization and maximization.
| Availability: | logtalk_load(local_optimization(loader))

| Author: Paulo Moura | Version: 1:0:0 | Date: 2026-08-24

| Compilation flags: | static, context_switching_calls

| Imports: | public :ref:`local_optimization_solver(Problem) <local_optimization_solver/1>` | Uses: | :ref:`linear_algebra <linear_algebra/0>` | :ref:`list <list/0>`

| Remarks:
- Subproblem: At each outer iteration, the step is obtained by approximately minimizing the local quadratic model within a ball of radius trust_radius, using the Steihaug-CG method (Nocedal and Wright, Algorithm 7.2): plain conjugate gradient on the model, terminated early either by a negative-curvature direction or by reaching the trust-region boundary, in which case the step is extended to the boundary along the current CG direction.
- No line search: Unlike the other gradient-based solvers in this library, this solver never backtracks a step size; the trust-region radius itself is grown or shrunk each iteration based on how well the quadratic model predicted the actual objective change, and a step is accepted only when that agreement is good enough.
- Internal minimization form: Maximization is handled by internally minimizing the negated objective, gradient, and Hessian, so the subproblem and acceptance test are always expressed in minimization form, which avoids sign errors.
- Convergence: Because it uses exact second-order information, this solver typically converges in far fewer iterations than gradient_descent(_), bfgs(_), or lbfgs(_) on well-behaved problems, at the cost of requiring an explicit hessian/2.
- Bounds: When the problem defines position_bounds/1, trial points are projected onto the box after each step. Projection can weaken the trust-region model agreement (the accepted step may differ from the one the subproblem solved for), which can trigger more radius shrinkage than an unconstrained problem would; a pure bound-constrained formulation is not implemented.
| Inherited public predicates: | Â :ref:`options_protocol/0::check_option/1` Â :ref:`options_protocol/0::check_options/1` Â :ref:`options_protocol/0::default_option/1` Â :ref:`options_protocol/0::default_options/1` Â :ref:`options_protocol/0::option/2` Â :ref:`options_protocol/0::option/3` Â :ref:`local_optimization_solver/1::run/2` Â :ref:`local_optimization_solver/1::run/3` Â :ref:`local_optimization_solver/1::run/4` Â :ref:`options_protocol/0::valid_option/1` Â :ref:`options_protocol/0::valid_options/1` Â

.. 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)

.. seealso::

:ref:`local_optimization_problem_protocol <local_optimization_problem_protocol/0>`, :ref:`local_optimization_solver(Problem) <local_optimization_solver/1>`, :ref:`gradient_descent(Problem) <gradient_descent/1>`, :ref:`conjugate_gradient(Problem) <conjugate_gradient/1>`, :ref:`bfgs(Problem) <bfgs/1>`, :ref:`lbfgs(Problem) <lbfgs/1>`