This algorithm realizes an estimation of the state of a system by minimization
of a cost function :math:`J` without gradient. It is a method that doesn't use
-the derivatives of the cost function. It fall for example in the same category
-then the :ref:`section_ref_algorithm_ParticleSwarmOptimization`.
+the derivatives of the cost function. It fall, for example, in the same category
+than the :ref:`section_ref_algorithm_ParticleSwarmOptimization`.
This is an optimization method allowing for global minimum search of a general
error function :math:`J` of type :math:`L^1`, :math:`L^2` or :math:`L^{\infty}`,
Minimizer
This key allows to choose the optimization minimizer. The default choice is
- "POWELL", and the possible ones are "POWELL" (modified Powell unconstrained
- minimizer, see [Powell]_), "SIMPLEX" (simplex or Nelder-Mead unconstrained
- minimizer, see [Nelder]_), "COBYLA" (constrained optimization by linear
- approximation). It is recommended to stay with the default when there is no
- bounds, and to choose "COBYLA" when there are bounds. Remark: the default
- "POWELL" method perform a dual outer/inner loops optimization, leading then
- to less control on the cost function evaluation number because it is the
- outer loop limit than is controled. If precise control on this cost function
- evaluation number is required, choose the "SIMPLEX" or the "COBYLA" one.
-
- Example : ``{"Minimizer":"POWELL"}``
+ "BOBYQA", and the possible ones are
+ "BOBYQA" (minimization with or without contraints by quadratic approximation [Powell09]_),
+ "COBYLA" (minimization with or without contraints by linear approximation [Powell94]_ [Powell98]_).
+ "NEWUOA" (minimization with or without contraints by iterative quadratic approximation [Powell04]_),
+ "POWELL" (minimization unconstrained using conjugate directions [Powell64]_),
+ "SIMPLEX" (minimization with or without contraints using Nelder-Mead simplex algorithm [Nelder65]_),
+ "SUBPLEX" (minimization with or without contraints using Nelder-Mead on a sequence of subspaces [Rowan90]_).
+ Remark: the "POWELL" method perform a dual outer/inner loops optimization,
+ leading then to less control on the cost function evaluation number because
+ it is the outer loop limit than is controled. If precise control on this
+ cost function evaluation number is required, choose an another minimizer.
+
+ Example : ``{"Minimizer":"BOBYQA"}``
MaximumNumberOfSteps
This key indicates the maximum number of iterations allowed for iterative
- :ref:`section_ref_algorithm_ParticleSwarmOptimization`
Bibliographical references:
- - [Nelder]_
- - [Powell]_
+ - [Johnson08]_
+ - [Nelder65]_
+ - [Powell64]_
+ - [Powell94]_
+ - [Powell98]_
+ - [Powell04]_
+ - [Powell07]_
+ - [Powell09]_
+ - [Rowan90]_