.. index:: single: nelder_mead(Problem)
.. _nelder_mead/1:

.. rst-class:: right

**object**

``nelder_mead(Problem)``
========================

* ``Problem`` - Problem object implementing ``local_optimization_problem_protocol``.


Nelder-Mead (downhill simplex) derivative-free local optimizer for continuous problems. Supports optional box constraints via projection, minimization and maximization, and the standard reflection / expansion / contraction / shrink operators.

| **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>`
|    :ref:`pairs <pairs/0>`

| **Remarks:**

   - Algorithm: Classic Nelder-Mead simplex method. An optional adaptive-parameter variant (Gao-Han) can be selected with the ``adaptive(true)`` option.
   - Bounds: When the problem defines ``position_bounds/1``, trial points are projected onto the box after every operator.
   - Initial simplex: Built from the problem ``initial_point/1`` by stepping along each coordinate axis. The step size is controlled by the ``initial_step(S)`` option (default 0.05 of each finite range, or an absolute 0.05 when unbounded).

| **Inherited public predicates:**
|     :ref:`options_protocol/0::check_option/1`  :ref:`options_protocol/0::check_options/1`  :ref:`options_protocol/0::default_option/1`  :ref:`options_protocol/0::default_options/1`  :ref:`options_protocol/0::option/2`  :ref:`options_protocol/0::option/3`  :ref:`local_optimization_solver/1::run/2`  :ref:`local_optimization_solver/1::run/3`  :ref:`local_optimization_solver/1::run/4`  :ref:`options_protocol/0::valid_option/1`  :ref:`options_protocol/0::valid_options/1`  

.. 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>`