.. [GilBellosta15] Gil Bellosta C. J., *rPython: Package Allowing R to Call Python*, CRAN, 2015, https://cran.r-project.org/web/packages/rPython/ and http://rpython.r-forge.r-project.org/
-.. [Bouttier99] Bouttier B., Courtier P., *Data assimilation concepts and methods*, Meteorological Training Course Lecture Series, ECMWF, 1999, http://www.ecmwf.int/sites/default/files/Data%20assimilation%20concepts%20and%20methods.pdf
+.. [Bouttier99] Bouttier B., Courtier P., *Data assimilation concepts and methods*, Meteorological Training Course Lecture Series, ECMWF, 1999
-.. [Bocquet04] Bocquet M., *Introduction aux principes et méthodes de l'assimilation de données en géophysique*, Lecture Notes, 2014, http://cerea.enpc.fr/HomePages/bocquet/Doc/assim-mb.pdf
+.. [Bocquet04] Bocquet M., *Introduction aux principes et méthodes de l'assimilation de données en géophysique*, Lecture Notes, 2014
.. [Buchinsky98] Buchinsky M., *Recent Advances in Quantile Regression Models: A Practical Guidline for Empirical Research*, Journal of Human Resources, 33(1), pp.88-126, 1998
.. [Ide97] Ide K., Courtier P., Ghil M., Lorenc A. C., *Unified notation for data assimilation: operational, sequential and variational*, Journal of the Meteorological Society of Japan, 75(1B), pp.181-189, 1997
+.. [Johnson08] Johnson S. G., *The NLopt nonlinear-optimization package*, http://ab-initio.mit.edu/nlopt
+
.. [Kalnay03] Kalnay E., *Atmospheric Modeling, Data Assimilation and Predictability*, Cambridge University Press, 2003
.. [Koenker00] Koenker R., Hallock K. F., *Quantile Regression: an Introduction*, 2000, http://www.econ.uiuc.edu/~roger/research/intro/intro.html
.. [Koenker01] Koenker R., Hallock K. F., *Quantile Regression*, Journal of Economic Perspectives, 15(4), pp.143-156, 2001
-.. [Morales11] Morales J.L., Nocedal J., *L-BFGS-B: Remark on Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization*, ACM Transactions on Mathematical Software, 38(1), 2011
+.. [Morales11] Morales J. L., Nocedal J., *L-BFGS-B: Remark on Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization*, ACM Transactions on Mathematical Software, 38(1), 2011
+
+.. [Nelder65] Nelder J. A., Mead R., *A simplex method for function minimization*, The Computer Journal, 7, pp.308-313, 1965
+
+.. [Powell64] Powell M. J. D., *An efficient method for finding the minimum of a function of several variables without calculating derivatives*, Computer Journal, 7(2), pp.155-162, 1964
+
+.. [Powell94] Powell M. J. D., *A direct search optimization method that models the objective and constraint functions by linear interpolation*, in Advances in Optimization and Numerical Analysis, eds. S. Gomez and J-P Hennart, Kluwer Academic (Dordrecht), pp. 51-67, 1994
-.. [Nelder] Nelder J.A., Mead R., *A simplex method for function minimization*, The Computer Journal, 7, pp.308-313, 1965
+.. [Powell98] Powell M. J. D., *Direct search algorithms for optimization calculations*, Acta Numerica 7, 287-336, 1998
-.. [Powell] Powell M.J.D., *An efficient method for finding the minimum of a function of several variables without calculating derivatives*, Computer Journal, 7(2), pp.155-162, 1964
+.. [Powell04] Powell M. J. D., *The NEWUOA software for unconstrained optimization without derivatives*, Proc. 40th Workshop on Large Scale Nonlinear Optimization, Erice, Italy, 2004
+
+.. [Powell07] Powell M. J. D., *A view of algorithms for optimization without derivatives*, Cambridge University Technical Report DAMTP 2007/NA03, 2007
+
+.. [Powell09] Powell M. J. D., *The BOBYQA algorithm for bound constrained optimization without derivatives*, Cambridge University Technical Report DAMTP NA2009/06, 2009
.. [R] *The R Project for Statistical Computing*, http://www.r-project.org/
+.. [Rowan90] Rowan T., *Functional Stability Analysis of Numerical Algorithms*, Ph.D. thesis, Department of Computer Sciences, University of Texas at Austin, 1990
+
.. [Salome] *SALOME The Open Source Integration Platform for Numerical Simulation*, http://www.salome-platform.org/
.. [SalomeMeca] *Salome_Meca and Code_Aster, Analysis of Structures and Thermomechanics for Studies & Research*, http://www.code-aster.org/
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]_
This algorithm realizes an estimation of the state of a dynamic system by
minimization of a cost function :math:`J` by using a particle swarm. It is a
method that doesn't use the derivatives of the cost function. It fall in the
-same category then the :ref:`section_ref_algorithm_DerivativeFreeOptimization`.
+same category than the :ref:`section_ref_algorithm_DerivativeFreeOptimization`.
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}`,
.. [GilBellosta15] Gil Bellosta C. J., *rPython: Package Allowing R to Call Python*, CRAN, 2015, https://cran.r-project.org/web/packages/rPython/ and http://rpython.r-forge.r-project.org/
-.. [Bouttier99] Bouttier B., Courtier P., *Data assimilation concepts and methods*, Meteorological Training Course Lecture Series, ECMWF, 1999, http://www.ecmwf.int/sites/default/files/Data%20assimilation%20concepts%20and%20methods.pdf
+.. [Bouttier99] Bouttier B., Courtier P., *Data assimilation concepts and methods*, Meteorological Training Course Lecture Series, ECMWF, 1999
-.. [Bocquet04] Bocquet M., *Introduction aux principes et méthodes de l'assimilation de données en géophysique*, Lecture Notes, 2014, http://cerea.enpc.fr/HomePages/bocquet/Doc/assim-mb.pdf
+.. [Bocquet04] Bocquet M., *Introduction aux principes et méthodes de l'assimilation de données en géophysique*, Lecture Notes, 2014
.. [Buchinsky98] Buchinsky M., *Recent Advances in Quantile Regression Models: A Practical Guidline for Empirical Research*, Journal of Human Resources, 33(1), pp.88-126, 1998
.. [Ide97] Ide K., Courtier P., Ghil M., Lorenc A. C., *Unified notation for data assimilation: operational, sequential and variational*, Journal of the Meteorological Society of Japan, 75(1B), pp.181-189, 1997
+.. [Johnson08] Johnson S. G., *The NLopt nonlinear-optimization package*, http://ab-initio.mit.edu/nlopt
+
.. [Kalnay03] Kalnay E., *Atmospheric Modeling, Data Assimilation and Predictability*, Cambridge University Press, 2003
.. [Koenker00] Koenker R., Hallock K. F., *Quantile Regression: an Introduction*, 2000, http://www.econ.uiuc.edu/~roger/research/intro/intro.html
.. [Koenker01] Koenker R., Hallock K. F., *Quantile Regression*, Journal of Economic Perspectives, 15(4), pp.143-156, 2001
-.. [Morales11] Morales J.L., Nocedal J., *L-BFGS-B: Remark on Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization*, ACM Transactions on Mathematical Software, 38(1), 2011
+.. [Morales11] Morales J. L., Nocedal J., *L-BFGS-B: Remark on Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization*, ACM Transactions on Mathematical Software, 38(1), 2011
+
+.. [Nelder65] Nelder J. A., Mead R., *A simplex method for function minimization*, The Computer Journal, 7, pp.308-313, 1965
+
+.. [Powell64] Powell M. J. D., *An efficient method for finding the minimum of a function of several variables without calculating derivatives*, Computer Journal, 7(2), pp.155-162, 1964
+
+.. [Powell94] Powell M. J. D., *A direct search optimization method that models the objective and constraint functions by linear interpolation*, in Advances in Optimization and Numerical Analysis, eds. S. Gomez and J-P Hennart, Kluwer Academic (Dordrecht), pp. 51-67, 1994
-.. [Nelder] Nelder J.A., Mead R., *A simplex method for function minimization*, The Computer Journal, 7, pp.308-313, 1965
+.. [Powell98] Powell M. J. D., *Direct search algorithms for optimization calculations*, Acta Numerica 7, 287-336, 1998
-.. [Powell] Powell M.J.D., *An efficient method for finding the minimum of a function of several variables without calculating derivatives*, Computer Journal, 7(2), pp.155-162, 1964
+.. [Powell04] Powell M. J. D., *The NEWUOA software for unconstrained optimization without derivatives*, Proc. 40th Workshop on Large Scale Nonlinear Optimization, Erice, Italy, 2004
+
+.. [Powell07] Powell M. J. D., *A view of algorithms for optimization without derivatives*, Cambridge University Technical Report DAMTP 2007/NA03, 2007
+
+.. [Powell09] Powell M. J. D., *The BOBYQA algorithm for bound constrained optimization without derivatives*, Cambridge University Technical Report DAMTP NA2009/06, 2009
.. [R] *The R Project for Statistical Computing*, http://www.r-project.org/
+.. [Rowan90] Rowan T., *Functional Stability Analysis of Numerical Algorithms*, Ph.D. thesis, Department of Computer Sciences, University of Texas at Austin, 1990
+
.. [Salome] *SALOME The Open Source Integration Platform for Numerical Simulation*, http://www.salome-platform.org/
.. [SalomeMeca] *Salome_Meca et Code_Aster, Analyse des Structures et Thermomécanique pour les Etudes et la Recherche*, http://www.code-aster.org/
Cet algorithme réalise une estimation d'état d'un système par minimisation d'une
fonctionnelle d'écart :math:`J` sans gradient. C'est une méthode qui n'utilise
-pas les dérivées de la fonctionnelle d'écart. Elle entre par exemple dans la
+pas les dérivées de la fonctionnelle d'écart. Elle entre, par exemple, dans la
même catégorie que l':ref:`section_ref_algorithm_ParticleSwarmOptimization`.
C'est une méthode d'optimisation permettant la recherche du minimum global d'une
Minimizer
Cette clé permet de changer le minimiseur pour l'optimiseur. Le choix par
- défaut est "POWELL", et les choix possibles sont "POWELL" (minimisation sans
- contraintes de type Powell modifiée, voir [Powell]_), "SIMPLEX"
- (minimisation sans contraintes de type simplexe ou Nelder-Mead, voir
- [Nelder]_), "COBYLA" (minimisation avec contraintes par approximation
- linéaire). Il est conseillé de conserver la valeur par défaut lorsqu'il n'y
- a pas de bornes, et de passer à "COBYLA" en cas de bornes. Remarque : la
- méthode par défaut "POWELL" effectue une optimisation par boucles imbriquées
- interne/externe, conduisant ainsi à un contrôle relaché du nombre
- d'évaluations de la fonctionnelle à optimiser. Si un contrôle précis du
- nombre d'évaluations de cette fonctionnelle est requis, il faut choisir
- "SIMPLEX" ou "COBYLA".
-
- Exemple : ``{"Minimizer":"POWELL"}``
+ défaut est "BOBYQA", et les choix possibles sont
+ "BOBYQA" (minimisation avec ou sans contraintes par approximation quadratique [Powell09]_),
+ "COBYLA" (minimisation avec ou sans contraintes par approximation linéaire [Powell94]_ [Powell98]_).
+ "NEWUOA" (minimisation avec ou sans contraintes par approximation quadratique itérative [Powell04]_),
+ "POWELL" (minimisation sans contraintes de type directions conjuguées [Powell64]_),
+ "SIMPLEX" (minimisation avec ou sans contraintes de type simplexe ou Nelder-Mead, voir [Nelder65]_),
+ "SUBPLEX" (minimisation avec ou sans contraintes de type simplexe sur une suite de sous-espaces [Rowan90]_).
+ Remarque : la méthode "POWELL" effectue une optimisation par boucles
+ imbriquées interne/externe, conduisant ainsi à un contrôle relaché du
+ nombre d'évaluations de la fonctionnelle à optimiser. Si un contrôle précis
+ du nombre d'évaluations de cette fonctionnelle est requis, il faut choisir
+ un autre minimiseur.
+
+ Exemple : ``{"Minimizer":"BOBYQA"}``
MaximumNumberOfSteps
Cette clé indique le nombre maximum d'itérations possibles en optimisation
- :ref:`section_ref_algorithm_ParticleSwarmOptimization`
Références bibliographiques :
- - [Nelder]_
- - [Powell]_
+ - [Johnson08]_
+ - [Nelder65]_
+ - [Powell64]_
+ - [Powell94]_
+ - [Powell98]_
+ - [Powell04]_
+ - [Powell07]_
+ - [Powell09]_
+ - [Rowan90]_
