doc/en/ref_algorithm_DerivativeFreeOptimization.rst

   1 ..
   2    Copyright (C) 2008-2024 EDF R&D
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  20    See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
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  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 .. ------------------------------------ ..
  31 .. include:: snippets/Header2Algo01.rst
  32
  33 This algorithm realizes an estimation of the state of a system by minimization
  34 without gradient of a cost function :math:`J`, using a search method by simplex
  35 type or similar approximation. It is a method that does not use the derivatives
  36 of the cost function. It falls in the same category than the
  37 :ref:`section_ref_algorithm_DifferentialEvolution`,
  38 :ref:`section_ref_algorithm_ParticleSwarmOptimization` or
  39 :ref:`section_ref_algorithm_TabuSearch`.
  40
  41 This is a mono-objective optimization method allowing for global minimum search
  42 of a general error function :math:`J` of type :math:`L^1`, :math:`L^2` or
  43 :math:`L^{\infty}`, with or without weights. The default error function is the
  44 augmented weighted least squares function, classically used in data
  45 assimilation.
  46
  47 .. ------------------------------------ ..
  48 .. include:: snippets/Header2Algo12.rst
  49
  50 .. include:: snippets/FeaturePropNonLocalOptimization.rst
  51
  52 .. include:: snippets/FeaturePropDerivativeFree.rst
  53
  54 .. include:: snippets/FeaturePropParallelFree.rst
  55
  56 .. include:: snippets/FeaturePropConvergenceOnBoth.rst
  57
  58 .. ------------------------------------ ..
  59 .. include:: snippets/Header2Algo02.rst
  60
  61 .. include:: snippets/Background.rst
  62
  63 .. include:: snippets/BackgroundError.rst
  64
  65 .. include:: snippets/Observation.rst
  66
  67 .. include:: snippets/ObservationError.rst
  68
  69 .. include:: snippets/ObservationOperator.rst
  70
  71 .. ------------------------------------ ..
  72 .. include:: snippets/Header2Algo03AdOp.rst
  73
  74 .. include:: snippets/Minimizer_DFO.rst
  75
  76 .. include:: snippets/BoundsWithNone.rst
  77
  78 .. include:: snippets/MaximumNumberOfIterations.rst
  79
  80 .. include:: snippets/MaximumNumberOfFunctionEvaluations.rst
  81
  82 .. include:: snippets/StateVariationTolerance.rst
  83
  84 .. include:: snippets/CostDecrementTolerance.rst
  85
  86 .. include:: snippets/QualityCriterion.rst
  87
  88 StoreSupplementaryCalculations
  89   .. index:: single: StoreSupplementaryCalculations
  90
  91   *List of names*. This list indicates the names of the supplementary
  92   variables, that can be available during or at the end of the algorithm, if
  93   they are initially required by the user. Their availability involves,
  94   potentially, costly calculations or memory consumptions. The default is then
  95   a void list, none of these variables being calculated and stored by default
  96   (excepted the unconditional variables). The possible names are in the
  97   following list (the detailed description of each named variable is given in
  98   the following part of this specific algorithmic documentation, in the
  99   sub-section "*Information and variables available at the end of the
 100   algorithm*"): [
 101   "Analysis",
 102   "BMA",
 103   "CostFunctionJ",
 104   "CostFunctionJb",
 105   "CostFunctionJo",
 106   "CostFunctionJAtCurrentOptimum",
 107   "CostFunctionJbAtCurrentOptimum",
 108   "CostFunctionJoAtCurrentOptimum",
 109   "CurrentIterationNumber",
 110   "CurrentOptimum",
 111   "CurrentState",
 112   "IndexOfOptimum",
 113   "Innovation",
 114   "InnovationAtCurrentState",
 115   "OMA",
 116   "OMB",
 117   "SimulatedObservationAtBackground",
 118   "SimulatedObservationAtCurrentOptimum",
 119   "SimulatedObservationAtCurrentState",
 120   "SimulatedObservationAtOptimum",
 121   ].
 122
 123   Example :
 124   ``{"StoreSupplementaryCalculations":["CurrentState", "Residu"]}``
 125
 126 .. ------------------------------------ ..
 127 .. include:: snippets/Header2Algo04.rst
 128
 129 .. include:: snippets/Analysis.rst
 130
 131 .. include:: snippets/CostFunctionJ.rst
 132
 133 .. include:: snippets/CostFunctionJb.rst
 134
 135 .. include:: snippets/CostFunctionJo.rst
 136
 137 .. include:: snippets/CurrentState.rst
 138
 139 .. ------------------------------------ ..
 140 .. include:: snippets/Header2Algo05.rst
 141
 142 .. include:: snippets/Analysis.rst
 143
 144 .. include:: snippets/BMA.rst
 145
 146 .. include:: snippets/CostFunctionJ.rst
 147
 148 .. include:: snippets/CostFunctionJb.rst
 149
 150 .. include:: snippets/CostFunctionJo.rst
 151
 152 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 153
 154 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 155
 156 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 157
 158 .. include:: snippets/CurrentIterationNumber.rst
 159
 160 .. include:: snippets/CurrentOptimum.rst
 161
 162 .. include:: snippets/CurrentState.rst
 163
 164 .. include:: snippets/IndexOfOptimum.rst
 165
 166 .. include:: snippets/Innovation.rst
 167
 168 .. include:: snippets/InnovationAtCurrentState.rst
 169
 170 .. include:: snippets/OMA.rst
 171
 172 .. include:: snippets/OMB.rst
 173
 174 .. include:: snippets/SimulatedObservationAtBackground.rst
 175
 176 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 177
 178 .. include:: snippets/SimulatedObservationAtCurrentState.rst
 179
 180 .. include:: snippets/SimulatedObservationAtOptimum.rst
 181
 182 .. ------------------------------------ ..
 183 .. _section_ref_algorithm_DerivativeFreeOptimization_examples:
 184
 185 .. include:: snippets/Header2Algo09.rst
 186
 187 .. include:: scripts/simple_DerivativeFreeOptimization.rst
 188
 189 .. literalinclude:: scripts/simple_DerivativeFreeOptimization.py
 190
 191 .. include:: snippets/Header2Algo10.rst
 192
 193 .. literalinclude:: scripts/simple_DerivativeFreeOptimization.res
 194     :language: none
 195
 196 .. include:: snippets/Header2Algo11.rst
 197
 198 .. _simple_DerivativeFreeOptimization:
 199 .. image:: scripts/simple_DerivativeFreeOptimization.png
 200   :align: center
 201   :width: 90%
 202
 203 .. ------------------------------------ ..
 204 .. include:: snippets/Header2Algo06.rst
 205
 206 - :ref:`section_ref_algorithm_ParticleSwarmOptimization`
 207 - :ref:`section_ref_algorithm_DifferentialEvolution`
 208 - :ref:`section_ref_algorithm_TabuSearch`
 209
 210 .. ------------------------------------ ..
 211 .. include:: snippets/Header2Algo07.rst
 212
 213 - [Johnson08]_
 214 - [Nelder65]_
 215 - [Powell64]_
 216 - [Powell94]_
 217 - [Powell98]_
 218 - [Powell04]_
 219 - [Powell07]_
 220 - [Powell09]_
 221 - [Rowan90]_
 222 - [WikipediaNM]_