BrentOptimizer (Apache Commons Math 3.3 API)

org.apache.commons.math3.optim.univariate

## Class BrentOptimizer

- java.lang.Object
- - org.apache.commons.math3.optim.BaseOptimizer<UnivariatePointValuePair>
  - - org.apache.commons.math3.optim.univariate.UnivariateOptimizer
    - - org.apache.commons.math3.optim.univariate.BrentOptimizer

-     public class BrentOptimizer
      extends UnivariateOptimizer

  For a function defined on some interval `(lo, hi)`, this class finds an approximation `x` to the point at which the function attains its minimum. It implements Richard Brent's algorithm (from his book "Algorithms for Minimization without Derivatives", p. 79) for finding minima of real univariate functions.
  This code is an adaptation, partly based on the Python code from SciPy (module "optimize.py" v0.5); the original algorithm is also modified
  - to use an initial guess provided by the user,
  - to ensure that the best point encountered is the one returned.
  Since:
    2.0
  Version:
    $Id: BrentOptimizer.java 1462503 2013-03-29 15:48:27Z luc $

- - ### Field Summary

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

      `evaluations, iterations`

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `BrentOptimizer(double rel, double abs)` The arguments are used for implementing the original stopping criterion of Brent's algorithm.
    `BrentOptimizer(double rel, double abs, ConvergenceChecker<UnivariatePointValuePair> checker)` The arguments are used implement the original stopping criterion of Brent's algorithm.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `protected UnivariatePointValuePair` | `doOptimize()` Performs the bulk of the optimization algorithm.

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

      `computeObjectiveValue, getGoalType, getMax, getMin, getStartValue, optimize, parseOptimizationData`

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

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

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

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

- - ### Constructor Detail

    - #### BrentOptimizer

          public BrentOptimizer(double rel,
                        double abs,
                        ConvergenceChecker<UnivariatePointValuePair> checker)

      The arguments are used implement the original stopping criterion of Brent's algorithm. `abs` and `rel` define a tolerance `tol = rel |x| + abs`. `rel` should be no smaller than 2 macheps and preferably not much less than sqrt(macheps), where macheps is the relative machine precision. `abs` must be positive.
      Parameters:
        `rel` - Relative threshold.
        `abs` - Absolute threshold.
        `checker` - Additional, user-defined, convergence checking procedure.
      Throws:
        `NotStrictlyPositiveException` - if `abs <= 0`.
        `NumberIsTooSmallException` - if `rel < 2 * Math.ulp(1d)`.

    - #### BrentOptimizer

          public BrentOptimizer(double rel,
                        double abs)

      The arguments are used for implementing the original stopping criterion of Brent's algorithm. `abs` and `rel` define a tolerance `tol = rel |x| + abs`. `rel` should be no smaller than 2 macheps and preferably not much less than sqrt(macheps), where macheps is the relative machine precision. `abs` must be positive.
      Parameters:
        `rel` - Relative threshold.
        `abs` - Absolute threshold.
      Throws:
        `NotStrictlyPositiveException` - if `abs <= 0`.
        `NumberIsTooSmallException` - if `rel < 2 * Math.ulp(1d)`.

  - ### Method Detail

    - #### doOptimize

          protected UnivariatePointValuePair doOptimize()

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

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