doc/en/ref_algorithm_DerivativeFreeOptimization.rst

   1 ..
   2    Copyright (C) 2008-2018 EDF R&D
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  20    See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
  21
  22    Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
  23
  24 .. index:: single: DerivativeFreeOptimization
  25 .. _section_ref_algorithm_DerivativeFreeOptimization:
  26
  27 Calculation algorithm "*DerivativeFreeOptimization*"
  28 ----------------------------------------------------
  29
  30 Description
  31 +++++++++++
  32
  33 This algorithm realizes an estimation of the state of a system by minimization
  34 of a cost function :math:`J` without gradient. It is a method that does not use
  35 the derivatives of the cost function. It falls in the same category than the
  36 :ref:`section_ref_algorithm_ParticleSwarmOptimization` or the
  37 :ref:`section_ref_algorithm_DifferentialEvolution`.
  38
  39 This is an optimization method allowing for global minimum search of a general
  40 error function :math:`J` of type :math:`L^1`, :math:`L^2` or :math:`L^{\infty}`,
  41 with or without weights. The default error function is the augmented weighted
  42 least squares function, classically used in data assimilation.
  43
  44 Optional and required commands
  45 ++++++++++++++++++++++++++++++
  46
  47 The general required commands, available in the editing user interface, are the
  48 following:
  49
  50   .. include:: snippets/Background.rst
  51
  52   .. include:: snippets/BackgroundError.rst
  53
  54   .. include:: snippets/Observation.rst
  55
  56   .. include:: snippets/ObservationError.rst
  57
  58   .. include:: snippets/ObservationOperator.rst
  59
  60 The general optional commands, available in the editing user interface, are
  61 indicated in :ref:`section_ref_assimilation_keywords`. Moreover, the parameters
  62 of the command "*AlgorithmParameters*" allows to choose the specific options,
  63 described hereafter, of the algorithm. See
  64 :ref:`section_ref_options_Algorithm_Parameters` for the good use of this
  65 command.
  66
  67 The options of the algorithm are the following:
  68
  69   .. include:: snippets/Minimizer_DFO.rst
  70
  71   .. include:: snippets/BoundsWithNone.rst
  72
  73   .. include:: snippets/MaximumNumberOfSteps.rst
  74
  75   .. include:: snippets/MaximumNumberOfFunctionEvaluations.rst
  76
  77   .. include:: snippets/StateVariationTolerance.rst
  78
  79   .. include:: snippets/CostDecrementTolerance.rst
  80
  81   .. include:: snippets/QualityCriterion.rst
  82
  83   StoreSupplementaryCalculations
  84     .. index:: single: StoreSupplementaryCalculations
  85
  86     This list indicates the names of the supplementary variables that can be
  87     available at the end of the algorithm. It involves potentially costly
  88     calculations or memory consumptions. The default is a void list, none of
  89     these variables being calculated and stored by default. The possible names
  90     are in the following list: ["BMA", "CostFunctionJ",
  91     "CostFunctionJAtCurrentOptimum", "CostFunctionJb",
  92     "CostFunctionJbAtCurrentOptimum", "CostFunctionJo",
  93     "CostFunctionJoAtCurrentOptimum", "CurrentOptimum", "CurrentState",
  94     "IndexOfOptimum", "Innovation", "InnovationAtCurrentState", "OMA", "OMB",
  95     "SimulatedObservationAtBackground", "SimulatedObservationAtCurrentOptimum",
  96     "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum"].
  97
  98     Example :
  99     ``{"StoreSupplementaryCalculations":["BMA", "Innovation"]}``
 100
 101 Information and variables available at the end of the algorithm
 102 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 103
 104 At the output, after executing the algorithm, there are variables and
 105 information originating from the calculation. The description of
 106 :ref:`section_ref_output_variables` show the way to obtain them by the method
 107 named ``get`` of the variable "*ADD*" of the post-processing. The input
 108 variables, available to the user at the output in order to facilitate the
 109 writing of post-processing procedures, are described in the
 110 :ref:`subsection_r_o_v_Inventaire`.
 111
 112 The unconditional outputs of the algorithm are the following:
 113
 114   .. include:: snippets/Analysis.rst
 115
 116   .. include:: snippets/CostFunctionJ.rst
 117
 118   .. include:: snippets/CostFunctionJb.rst
 119
 120   .. include:: snippets/CostFunctionJo.rst
 121
 122   .. include:: snippets/CurrentState.rst
 123
 124 The conditional outputs of the algorithm are the following:
 125
 126   .. include:: snippets/BMA.rst
 127
 128   .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 129
 130   .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 131
 132   .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 133
 134   .. include:: snippets/CurrentOptimum.rst
 135
 136   .. include:: snippets/IndexOfOptimum.rst
 137
 138   .. include:: snippets/Innovation.rst
 139
 140   .. include:: snippets/InnovationAtCurrentState.rst
 141
 142   .. include:: snippets/OMA.rst
 143
 144   .. include:: snippets/OMB.rst
 145
 146   .. include:: snippets/SimulatedObservationAtBackground.rst
 147
 148   .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 149
 150   .. include:: snippets/SimulatedObservationAtCurrentState.rst
 151
 152   .. include:: snippets/SimulatedObservationAtOptimum.rst
 153
 154 See also
 155 ++++++++
 156
 157 References to other sections:
 158   - :ref:`section_ref_algorithm_ParticleSwarmOptimization`
 159   - :ref:`section_ref_algorithm_DifferentialEvolution`
 160
 161 Bibliographical references:
 162   - [Johnson08]_
 163   - [Nelder65]_
 164   - [Powell64]_
 165   - [Powell94]_
 166   - [Powell98]_
 167   - [Powell04]_
 168   - [Powell07]_
 169   - [Powell09]_
 170   - [Rowan90]_