`barzilai_borwein(Problem)`

Problem - Problem object implementing local_optimization_problem_protocol and defining gradient/2. Barzilai-Borwein (BB) gradient method with adaptive step sizes. Requires the problem to define gradient/2. Supports box constraints via projection, minimization and maximization, and BB1 / BB2 / alternating formulas.
| Availability: | logtalk_load(local_optimization(loader))

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

| 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:
- Step formulas: formula(bb1) uses alpha = (s*s)/(s*y) (long step). formula(bb2) uses alpha = (s*y)/(y*y) (short step). formula(alternate) (default) switches between BB1 and BB2 each iteration.
- Safeguards: When the denominator is near zero or the computed step is outside [step_min, step_max], the previous accepted step (or step_size on the first iteration) is reused.
- Line search: Optional non-monotone Armijo acceptance controlled by line_search(none|armijo). The default none accepts the pure BB step.
- Bounds: When the problem defines position_bounds/1, trial points are projected onto the box after each step.
| 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:`nelder_mead(Problem) <nelder_mead/1>`