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

java.lang.Object
  extended by org.apache.commons.math3.optim.BaseOptimizer<PAIR>
      extended by org.apache.commons.math3.optim.BaseMultivariateOptimizer<PointValuePair>
          extended by org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer
              extended by org.apache.commons.math3.optim.nonlinear.scalar.noderiv.PowellOptimizer

public class PowellOptimizer
extends MultivariateOptimizer

Powell's algorithm. This code is translated and adapted from the Python version of this algorithm (as implemented in module optimize.py v0.5 of SciPy).
The default stopping criterion is based on the differences of the function value between two successive iterations. It is however possible to define a custom convergence checker that might terminate the algorithm earlier.
The internal line search optimizer is a BrentOptimizer with a convergence checker set to SimpleUnivariateValueChecker.
Constraints are not supported: the call to optimize will throw MathUnsupportedOperationException if bounds are passed to it. In order to impose simple constraints, the objective function must be wrapped in an adapter like MultivariateFunctionMappingAdapter or MultivariateFunctionPenaltyAdapter.

Since:
2.2
Version:
$Id: PowellOptimizer.java 1462503 2013-03-29 15:48:27Z luc $

Nested Class Summary
private  class PowellOptimizer.LineSearch
          Class for finding the minimum of the objective function along a given direction.
 
Field Summary
private  double absoluteThreshold
          Absolute threshold.
private  PowellOptimizer.LineSearch line
          Line search.
private static double MIN_RELATIVE_TOLERANCE
          Minimum relative tolerance.
private  double relativeThreshold
          Relative threshold.
 
Fields inherited from class org.apache.commons.math3.optim.BaseOptimizer
evaluations, iterations
 
Constructor Summary
PowellOptimizer(double rel, double abs)
          The parameters control the default convergence checking procedure.
PowellOptimizer(double rel, double abs, ConvergenceChecker<PointValuePair> checker)
          This constructor allows to specify a user-defined convergence checker, in addition to the parameters that control the default convergence checking procedure.
PowellOptimizer(double rel, double abs, double lineRel, double lineAbs)
          Builds an instance with the default convergence checking procedure.
PowellOptimizer(double rel, double abs, double lineRel, double lineAbs, ConvergenceChecker<PointValuePair> checker)
          This constructor allows to specify a user-defined convergence checker, in addition to the parameters that control the default convergence checking procedure and the line search tolerances.
 
Method Summary
private  void checkParameters()
           
protected  PointValuePair doOptimize()
          Performs the bulk of the optimization algorithm.
private  double[][] newPointAndDirection(double[] p, double[] d, double optimum)
          Compute a new point (in the original space) and a new direction vector, resulting from the line search.
 
Methods inherited from class org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer
computeObjectiveValue, getGoalType, optimize, parseOptimizationData
 
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

MIN_RELATIVE_TOLERANCE

private static final double MIN_RELATIVE_TOLERANCE
Minimum relative tolerance.


relativeThreshold

private final double relativeThreshold
Relative threshold.


absoluteThreshold

private final double absoluteThreshold
Absolute threshold.


line

private final PowellOptimizer.LineSearch line
Line search.

Constructor Detail

PowellOptimizer

public PowellOptimizer(double rel,
                       double abs,
                       ConvergenceChecker<PointValuePair> checker)
This constructor allows to specify a user-defined convergence checker, in addition to the parameters that control the default convergence checking procedure.
The internal line search tolerances are set to the square-root of their corresponding value in the multivariate optimizer.

Parameters:
rel - Relative threshold.
abs - Absolute threshold.
checker - Convergence checker.
Throws:
NotStrictlyPositiveException - if abs <= 0.
NumberIsTooSmallException - if rel < 2 * Math.ulp(1d).

PowellOptimizer

public PowellOptimizer(double rel,
                       double abs,
                       double lineRel,
                       double lineAbs,
                       ConvergenceChecker<PointValuePair> checker)
This constructor allows to specify a user-defined convergence checker, in addition to the parameters that control the default convergence checking procedure and the line search tolerances.

Parameters:
rel - Relative threshold for this optimizer.
abs - Absolute threshold for this optimizer.
lineRel - Relative threshold for the internal line search optimizer.
lineAbs - Absolute threshold for the internal line search optimizer.
checker - Convergence checker.
Throws:
NotStrictlyPositiveException - if abs <= 0.
NumberIsTooSmallException - if rel < 2 * Math.ulp(1d).

PowellOptimizer

public PowellOptimizer(double rel,
                       double abs)
The parameters control the default convergence checking procedure.
The internal line search tolerances are set to the square-root of their corresponding value in the multivariate optimizer.

Parameters:
rel - Relative threshold.
abs - Absolute threshold.
Throws:
NotStrictlyPositiveException - if abs <= 0.
NumberIsTooSmallException - if rel < 2 * Math.ulp(1d).

PowellOptimizer

public PowellOptimizer(double rel,
                       double abs,
                       double lineRel,
                       double lineAbs)
Builds an instance with the default convergence checking procedure.

Parameters:
rel - Relative threshold.
abs - Absolute threshold.
lineRel - Relative threshold for the internal line search optimizer.
lineAbs - Absolute threshold for the internal line search optimizer.
Throws:
NotStrictlyPositiveException - if abs <= 0.
NumberIsTooSmallException - if rel < 2 * Math.ulp(1d).
Method Detail

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.

newPointAndDirection

private double[][] newPointAndDirection(double[] p,
                                        double[] d,
                                        double optimum)
Compute a new point (in the original space) and a new direction vector, resulting from the line search.

Parameters:
p - Point used in the line search.
d - Direction used in the line search.
optimum - Optimum found by the line search.
Returns:
a 2-element array containing the new point (at index 0) and the new direction (at index 1).

checkParameters

private void checkParameters()
Throws:
MathUnsupportedOperationException - if bounds were passed to the optimize method.


Copyright (c) 2003-2013 Apache Software Foundation