org.apache.commons.math3.optim.nonlinear.scalar.noderiv

## Class SimplexOptimizer

- java.lang.Object
- - org.apache.commons.math3.optim.BaseOptimizer<PAIR>
  - - org.apache.commons.math3.optim.BaseMultivariateOptimizer<PointValuePair>
    - - org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer
      - - org.apache.commons.math3.optim.nonlinear.scalar.noderiv.SimplexOptimizer

-     public class SimplexOptimizer
      extends MultivariateOptimizer

  This class implements simplex-based direct search optimization.

  Direct search methods only use objective function values, they do not need derivatives and don't either try to compute approximation of the derivatives. According to a 1996 paper by Margaret H. Wright (Direct Search Methods: Once Scorned, Now Respectable), they are used when either the computation of the derivative is impossible (noisy functions, unpredictable discontinuities) or difficult (complexity, computation cost). In the first cases, rather than an optimum, a not too bad point is desired. In the latter cases, an optimum is desired but cannot be reasonably found. In all cases direct search methods can be useful.

  Simplex-based direct search methods are based on comparison of the objective function values at the vertices of a simplex (which is a set of n+1 points in dimension n) that is updated by the algorithms steps.

  The simplex update procedure (`NelderMeadSimplex` or `MultiDirectionalSimplex`) must be passed to the `optimize` method.

  Each call to `optimize` will re-use the start configuration of the current simplex and move it such that its first vertex is at the provided start point of the optimization. If the `optimize` method is called to solve a different problem and the number of parameters change, the simplex must be re-initialized to one with the appropriate dimensions.

  Convergence is checked by providing the worst points of previous and current simplex to the convergence checker, not the best ones.

  This simplex optimizer implementation does not directly support constrained optimization with simple bounds; so, for such optimizations, either a more dedicated algorithm must be used like `CMAESOptimizer` or `BOBYQAOptimizer`, or the objective function must be wrapped in an adapter like `MultivariateFunctionMappingAdapter` or `MultivariateFunctionPenaltyAdapter`.

  Since:
    3.0
  Version:
    $Id: SimplexOptimizer.java 1397759 2012-10-13 01:12:58Z erans $

- - ### Field Summary

    Fields
    Modifier and Type | Field and Description
    --- | ---
    `private AbstractSimplex` | `simplex` Simplex update rule.

    - ### Fields inherited from class org.apache.commons.math3.optim.BaseOptimizer

      `evaluations, iterations`

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `SimplexOptimizer(ConvergenceChecker<PointValuePair> checker)`
    `SimplexOptimizer(double rel, double abs)`

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `protected PointValuePair` | `doOptimize()` Performs the bulk of the optimization algorithm.
    `PointValuePair` | `optimize(OptimizationData... optData)` Stores data and performs the optimization.
    `private void` | `parseOptimizationData(OptimizationData... optData)` Scans the list of (required and optional) optimization data that characterize the problem.

    - ### Methods inherited from class org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer

      `computeObjectiveValue, getGoalType`

    - ### Methods inherited from class org.apache.commons.math3.optim.BaseMultivariateOptimizer

      `getLowerBound, getStartPoint, getUpperBound`

    - ### Methods inherited from class org.apache.commons.math3.optim.BaseOptimizer

      `getConvergenceChecker, getEvaluations, getIterations, getMaxEvaluations, getMaxIterations, incrementEvaluationCount, incrementIterationCount`

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### Field Detail

    - #### simplex

          private AbstractSimplex simplex

      Simplex update rule.

  - ### Constructor Detail

    - #### SimplexOptimizer

          public SimplexOptimizer(ConvergenceChecker<PointValuePair> checker)

      Parameters:
        `checker` - Convergence checker.

    - #### SimplexOptimizer

          public SimplexOptimizer(double rel,
                          double abs)

      Parameters:
        `rel` - Relative threshold.
        `abs` - Absolute threshold.

  - ### Method Detail

    - #### optimize

          public PointValuePair optimize(OptimizationData... optData)

      Stores data and performs the optimization.
      Overrides:
        `optimize` in class `MultivariateOptimizer`
      Parameters:
        `optData` - Optimization data. The following data will be looked for:
        - `MaxEval`
        - `InitialGuess`
        - `SimpleBounds`
        - `AbstractSimplex`
      Returns:
        a point/value pair that satifies the convergence criteria.

    - #### doOptimize

          protected PointValuePair doOptimize()

      Performs the bulk of the optimization algorithm.
      Specified by:
        `doOptimize` in class `BaseOptimizer<PointValuePair>`
      Returns:
        the point/value pair giving the optimal value of the objective function.

    - #### parseOptimizationData

          private void parseOptimizationData(OptimizationData... optData)

      Scans the list of (required and optional) optimization data that characterize the problem.
      Parameters:
        `optData` - Optimization data. The following data will be looked for:
        - `AbstractSimplex`

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