.. index:: single: gradient_descent(Problem) .. _gradient_descent/1:

.. rst-class:: right

object

gradient_descent(Problem)

• Problem - Problem object implementing local_optimization_problem_protocol and defining gradient/2. Gradient descent (steepest descent) local optimizer with optional backtracking Armijo line search. Requires the problem to define gradient/2. Supports box constraints via projection, minimization and maximization.

  | 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:

  • Line search: The line_search(armijo) option (default) uses backtracking Armijo line search. The line_search(fixed) option uses a constant step size given by step_size(S).
  • Bounds: When the problem defines position_bounds/1, the gradient step is projected onto the box (projected gradient descent).
  • Direction: For minimization the search direction is -gradient; for maximization it is +gradient.

  | 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:`bfgs(Problem) <bfgs/1>`, :ref:`conjugate_gradient(Problem) <conjugate_gradient/1>`, :ref:`nelder_mead(Problem) <nelder_mead/1>`