Modifier and Type	Class and Description
public static class	NonLinearConjugateGradientOptimizer.BracketingStep Deprecated As of v3.3, this class is not used anymore. This setting is replaced by the `initialBracketingRange` argument to the new constructors. The initial step is a factor with respect to the search direction (which itself is roughly related to the gradient of the function).
public static enum	NonLinearConjugateGradientOptimizer.Formula Available choices of update formulas for the updating the parameter that is used to compute the successive conjugate search directions.
public static class	NonLinearConjugateGradientOptimizer.IdentityPreconditioner Default identity preconditioner.

Modifier and Type	Field and Description
private final LineSearch	line Line search algorithm.
private final Preconditioner	preconditioner Preconditioner (may be null).
private final NonLinearConjugateGradientOptimizer.Formula	updateFormula Update formula for the beta parameter.

Constructor Summary

Access	Constructor and Description
public	NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula formula to use for updating the β parameter, must be one of `Formula#FLETCHER_REEVES` or `Formula#POLAK_RIBIERE`. updateFormula, ConvergenceChecker<PointValuePair> Convergence checker. checker) Constructor with default tolerances for the line search (1e-8) and `preconditioner`.
public	NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula formula to use for updating the β parameter, must be one of `Formula#FLETCHER_REEVES` or `Formula#POLAK_RIBIERE`. updateFormula, ConvergenceChecker<PointValuePair> Convergence checker. checker, final UnivariateSolver Solver to use during line search. lineSearchSolver) Deprecated as of 3.3. Constructor with default `preconditioner`.
public	NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula formula to use for updating the β parameter, must be one of `Formula#FLETCHER_REEVES` or `Formula#POLAK_RIBIERE`. updateFormula, ConvergenceChecker<PointValuePair> Convergence checker. checker, double Relative threshold for line search. relativeTolerance, double Absolute threshold for line search. absoluteTolerance, double Extent of the initial interval used to find an interval that brackets the optimum in order to perform the line search. initialBracketingRange) Constructor with default `preconditioner`.
public	NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula formula to use for updating the β parameter, must be one of `Formula#FLETCHER_REEVES` or `Formula#POLAK_RIBIERE`. updateFormula, ConvergenceChecker<PointValuePair> Convergence checker. checker, final UnivariateSolver Solver to use during line search. lineSearchSolver, final Preconditioner Preconditioner. preconditioner) Deprecated as of 3.3.
public	NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula formula to use for updating the β parameter, must be one of `Formula#FLETCHER_REEVES` or `Formula#POLAK_RIBIERE`. updateFormula, ConvergenceChecker<PointValuePair> Convergence checker. checker, double Relative threshold for line search. relativeTolerance, double Absolute threshold for line search. absoluteTolerance, double Extent of the initial interval used to find an interval that brackets the optimum in order to perform the line search. initialBracketingRange, final Preconditioner Preconditioner. preconditioner)

Method Summary

Modifier and Type	Method and Description
private void	checkParameters() Hides org.apache.commons.math3.optim.BaseMultivariateOptimizer.checkParameters. Check parameters consistency.
protected PointValuePair	doOptimize() Implements abstract org.apache.commons.math3.optim.BaseOptimizer.doOptimize. Performs the bulk of the optimization algorithm.
public PointValuePair	optimize(OptimizationData... Optimization data. In addition to those documented in `MultivariateOptimizer`, this method will register the following data: `ObjectiveFunctionGradient` optData) Overrides org.apache.commons.math3.optim.nonlinear.scalar.GradientMultivariateOptimizer.optimize. Stores data and performs the optimization.
protected void	parseOptimizationData(OptimizationData... Optimization data. The following data will be looked for: `ObjectiveFunctionGradient` optData) Overrides org.apache.commons.math3.optim.nonlinear.scalar.GradientMultivariateOptimizer.parseOptimizationData. Scans the list of (required and optional) optimization data that characterize the problem.

Inherited from org.apache.commons.math3.optim.nonlinear.scalar.GradientMultivariateOptimizer:: computeObjectiveGradient

Field Detail

line	back to summary
private final LineSearch line Line search algorithm.

preconditioner	back to summary
private final Preconditioner preconditioner Preconditioner (may be null).

updateFormula	back to summary
private final NonLinearConjugateGradientOptimizer.Formula updateFormula Update formula for the beta parameter.

Constructor Detail

NonLinearConjugateGradientOptimizer back to summary

NonLinearConjugateGradientOptimizer	back to summary
public NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula updateFormula, ConvergenceChecker<PointValuePair> checker) Constructor with default tolerances for the line search (1e-8) and `preconditioner`. Parameters updateFormula:NonLinearConjugateGradientOptimizer.Formula formula to use for updating the β parameter, must be one of `Formula#FLETCHER_REEVES` or `Formula#POLAK_RIBIERE`. checker:ConvergenceChecker<PointValuePair> Convergence checker.

public NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula updateFormula, ConvergenceChecker<PointValuePair> checker)

Constructor with default tolerances for the line search (1e-8) and preconditioner.

Parameters

updateFormula:NonLinearConjugateGradientOptimizer.Formula: formula to use for updating the β parameter, must be one of Formula#FLETCHER_REEVES or Formula#POLAK_RIBIERE.
checker:ConvergenceChecker<PointValuePair>: Convergence checker.

NonLinearConjugateGradientOptimizer back to summary

NonLinearConjugateGradientOptimizer	back to summary
public NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula updateFormula, ConvergenceChecker<PointValuePair> checker, final UnivariateSolver lineSearchSolver) Deprecated as of 3.3. Please use `NonLinearConjugateGradientOptimizer(Formula, ConvergenceChecker, double, double, double)` instead. Constructor with default `preconditioner`. Parameters updateFormula:NonLinearConjugateGradientOptimizer.Formula formula to use for updating the β parameter, must be one of `Formula#FLETCHER_REEVES` or `Formula#POLAK_RIBIERE`. checker:ConvergenceChecker<PointValuePair> Convergence checker. lineSearchSolver:UnivariateSolver Solver to use during line search. Annotations @Deprecated

public NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula updateFormula, ConvergenceChecker<PointValuePair> checker, final UnivariateSolver lineSearchSolver)

Deprecated

as of 3.3. Please use NonLinearConjugateGradientOptimizer(Formula, ConvergenceChecker, double, double, double) instead.

Constructor with default preconditioner.

Parameters

updateFormula:NonLinearConjugateGradientOptimizer.Formula: formula to use for updating the β parameter, must be one of Formula#FLETCHER_REEVES or Formula#POLAK_RIBIERE.
checker:ConvergenceChecker<PointValuePair>: Convergence checker.
lineSearchSolver:UnivariateSolver: Solver to use during line search.

Annotations

@Deprecated

NonLinearConjugateGradientOptimizer back to summary

NonLinearConjugateGradientOptimizer	back to summary
public NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula updateFormula, ConvergenceChecker<PointValuePair> checker, double relativeTolerance, double absoluteTolerance, double initialBracketingRange) Constructor with default `preconditioner`. Parameters updateFormula:NonLinearConjugateGradientOptimizer.Formula formula to use for updating the β parameter, must be one of `Formula#FLETCHER_REEVES` or `Formula#POLAK_RIBIERE`. checker:ConvergenceChecker<PointValuePair> Convergence checker. relativeTolerance:double Relative threshold for line search. absoluteTolerance:double Absolute threshold for line search. initialBracketingRange:double Extent of the initial interval used to find an interval that brackets the optimum in order to perform the line search. Since 3.3 See Also `LineSearch#LineSearch(MultivariateOptimizer, double, double, double)`

public NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula updateFormula, ConvergenceChecker<PointValuePair> checker, double relativeTolerance, double absoluteTolerance, double initialBracketingRange)

Constructor with default preconditioner.

Parameters

updateFormula:NonLinearConjugateGradientOptimizer.Formula: formula to use for updating the β parameter, must be one of Formula#FLETCHER_REEVES or Formula#POLAK_RIBIERE.
checker:ConvergenceChecker<PointValuePair>: Convergence checker.
relativeTolerance:double: Relative threshold for line search.
absoluteTolerance:double: Absolute threshold for line search.
initialBracketingRange:double: Extent of the initial interval used to find an interval that brackets the optimum in order to perform the line search.

Since

3.3

NonLinearConjugateGradientOptimizer back to summary

NonLinearConjugateGradientOptimizer	back to summary
public NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula updateFormula, ConvergenceChecker<PointValuePair> checker, final UnivariateSolver lineSearchSolver, final Preconditioner preconditioner) Deprecated as of 3.3. Please use `NonLinearConjugateGradientOptimizer(Formula, ConvergenceChecker, double, double, double, Preconditioner)` instead. Parameters updateFormula:NonLinearConjugateGradientOptimizer.Formula formula to use for updating the β parameter, must be one of `Formula#FLETCHER_REEVES` or `Formula#POLAK_RIBIERE`. checker:ConvergenceChecker<PointValuePair> Convergence checker. lineSearchSolver:UnivariateSolver Solver to use during line search. preconditioner:Preconditioner Preconditioner. Annotations @Deprecated

public NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula updateFormula, ConvergenceChecker<PointValuePair> checker, final UnivariateSolver lineSearchSolver, final Preconditioner preconditioner)

Deprecated

as of 3.3. Please use NonLinearConjugateGradientOptimizer(Formula, ConvergenceChecker, double, double, double, Preconditioner) instead.

Parameters

updateFormula:NonLinearConjugateGradientOptimizer.Formula: formula to use for updating the β parameter, must be one of Formula#FLETCHER_REEVES or Formula#POLAK_RIBIERE.
checker:ConvergenceChecker<PointValuePair>: Convergence checker.
lineSearchSolver:UnivariateSolver: Solver to use during line search.
preconditioner:Preconditioner: Preconditioner.

Annotations

@Deprecated

NonLinearConjugateGradientOptimizer back to summary

NonLinearConjugateGradientOptimizer	back to summary
public NonLinearConjugateGradientOptimizer(final NonLinearConjugateGradientOptimizer.Formula updateFormula, ConvergenceChecker<PointValuePair> checker, double relativeTolerance, double absoluteTolerance, double initialBracketingRange, final Preconditioner preconditioner) Parameters updateFormula:NonLinearConjugateGradientOptimizer.Formula formula to use for updating the β parameter, must be one of `Formula#FLETCHER_REEVES` or `Formula#POLAK_RIBIERE`. checker:ConvergenceChecker<PointValuePair> Convergence checker. relativeTolerance:double Relative threshold for line search. absoluteTolerance:double Absolute threshold for line search. initialBracketingRange:double Extent of the initial interval used to find an interval that brackets the optimum in order to perform the line search. preconditioner:Preconditioner Preconditioner. Since 3.3 See Also `LineSearch#LineSearch(MultivariateOptimizer, double, double, double)`

Parameters

updateFormula:NonLinearConjugateGradientOptimizer.Formula: formula to use for updating the β parameter, must be one of Formula#FLETCHER_REEVES or Formula#POLAK_RIBIERE.
checker:ConvergenceChecker<PointValuePair>: Convergence checker.
relativeTolerance:double: Relative threshold for line search.
absoluteTolerance:double: Absolute threshold for line search.
initialBracketingRange:double: Extent of the initial interval used to find an interval that brackets the optimum in order to perform the line search.
preconditioner:Preconditioner: Preconditioner.

Since

3.3

Method Detail

checkParameters back to summary

checkParameters	back to summary
private void checkParameters() Hides org.apache.commons.math3.optim.BaseMultivariateOptimizer.checkParameters. Doc from org.apache.commons.math3.optim.BaseMultivariateOptimizer.checkParameters. Check parameters consistency. Exceptions MathUnsupportedOperationException: if bounds were passed to the `optimize` method.

private void checkParameters()

Hides org.apache.commons.math3.optim.BaseMultivariateOptimizer.checkParameters.

Doc from org.apache.commons.math3.optim.BaseMultivariateOptimizer.checkParameters.

Check parameters consistency.

Exceptions

MathUnsupportedOperationException:: if bounds were passed to the optimize method.

doOptimize	back to summary
protected PointValuePair doOptimize() Implements abstract org.apache.commons.math3.optim.BaseOptimizer.doOptimize. Doc from org.apache.commons.math3.optim.BaseOptimizer.doOptimize. Performs the bulk of the optimization algorithm. Returns:PointValuePair the point/value pair giving the optimal value of the objective function. Annotations @Override

doOptimize

back to summary

protected PointValuePair doOptimize()

Implements abstract org.apache.commons.math3.optim.BaseOptimizer.doOptimize.

Doc from org.apache.commons.math3.optim.BaseOptimizer.doOptimize.

Performs the bulk of the optimization algorithm.

Returns:PointValuePair

the point/value pair giving the optimal value of the objective function.

Annotations

@Override

optimize back to summary

optimize	back to summary
public PointValuePair optimize(OptimizationData... optData) throws TooManyEvaluationsException Overrides org.apache.commons.math3.optim.nonlinear.scalar.GradientMultivariateOptimizer.optimize. Doc from org.apache.commons.math3.optim.nonlinear.scalar.GradientMultivariateOptimizer.optimize. Stores data and performs the optimization. The list of parameters is open-ended so that sub-classes can extend it with arguments specific to their concrete implementations. When the method is called multiple times, instance data is overwritten only when actually present in the list of arguments: when not specified, data set in a previous call is retained (and thus is optional in subsequent calls). Important Note Subclasses must override `parseOptimizationData(OptimizationData[])` if they need to register their own options; but then, they must also call `super.parseOptimizationData(optData)` within that method. Parameters optData:OptimizationData[] Optimization data. In addition to those documented in `MultivariateOptimizer`, this method will register the following data: `ObjectiveFunctionGradient` Returns:PointValuePair a point/value pair that satisfies the convergence criteria. Annotations @Override Exceptions TooManyEvaluationsException: if the maximal number of evaluations (of the objective function) is exceeded.

public PointValuePair optimize(OptimizationData... optData) throws TooManyEvaluationsException

Overrides org.apache.commons.math3.optim.nonlinear.scalar.GradientMultivariateOptimizer.optimize.

Doc from org.apache.commons.math3.optim.nonlinear.scalar.GradientMultivariateOptimizer.optimize.

Stores data and performs the optimization.

The list of parameters is open-ended so that sub-classes can extend it with arguments specific to their concrete implementations.

When the method is called multiple times, instance data is overwritten only when actually present in the list of arguments: when not specified, data set in a previous call is retained (and thus is optional in subsequent calls).

Important Note

Subclasses must override parseOptimizationData(OptimizationData[]) if they need to register their own options; but then, they must also call super.parseOptimizationData(optData) within that method.

Parameters

optData:OptimizationData[]

Optimization data. In addition to those documented in MultivariateOptimizer, this method will register the following data:

ObjectiveFunctionGradient

Returns:PointValuePair

a point/value pair that satisfies the convergence criteria.

Annotations

@Override

Exceptions

TooManyEvaluationsException:: if the maximal number of evaluations (of the objective function) is exceeded.

parseOptimizationData back to summary

parseOptimizationData	back to summary
protected void parseOptimizationData(OptimizationData... optData) Overrides org.apache.commons.math3.optim.nonlinear.scalar.GradientMultivariateOptimizer.parseOptimizationData. Doc from org.apache.commons.math3.optim.nonlinear.scalar.GradientMultivariateOptimizer.parseOptimizationData. Scans the list of (required and optional) optimization data that characterize the problem. Parameters optData:OptimizationData[] Optimization data. The following data will be looked for: `ObjectiveFunctionGradient` Annotations @Override

protected void parseOptimizationData(OptimizationData... optData)

Overrides org.apache.commons.math3.optim.nonlinear.scalar.GradientMultivariateOptimizer.parseOptimizationData.

Doc from org.apache.commons.math3.optim.nonlinear.scalar.GradientMultivariateOptimizer.parseOptimizationData.

Scans the list of (required and optional) optimization data that characterize the problem.

Parameters

optData:OptimizationData[]

Optimization data. The following data will be looked for:

ObjectiveFunctionGradient

Annotations

@Override

org.apache.commons.math3.optim.nonlinear.scalar.gradient back to summary

public Class NonLinearConjugateGradientOptimizer.BracketingStep

Class Inheritance

extends Object
implements OptimizationData

java.lang.Object
org.apache.commons.math3.optim.nonlinear.scalar.gradient.NonLinearConjugateGradientOptimizer.BracketingStep

All Implemented Interfaces

org.apache.commons.math3.optim.OptimizationData

Annotations

@Deprecated

Deprecated

As of v3.3, this class is not used anymore. This setting is replaced by the initialBracketingRange argument to the new constructors.

The initial step is a factor with respect to the search direction (which itself is roughly related to the gradient of the function).
It is used to find an interval that brackets the optimum in line search.

Since: 3.1

Field Summary

Modifier and Type	Field and Description
private final double	initialStep Initial step.

Constructor Summary

Access	Constructor and Description
public	BracketingStep(double Initial step for the bracket search. step)

Method Summary

Modifier and Type	Method and Description
public double	Returns: the initial step. getBracketingStep() Gets the initial step.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

initialStep	back to summary
private final double initialStep Initial step.

Constructor Detail

BracketingStep	back to summary
public BracketingStep(double step) Parameters step:double Initial step for the bracket search.

Method Detail

getBracketingStep	back to summary
public double getBracketingStep() Gets the initial step. Returns:double the initial step.

getBracketingStep

back to summary

public double getBracketingStep()

Gets the initial step.

Returns:double: the initial step.

org.apache.commons.math3.optim.nonlinear.scalar.gradient back to summary

public final Enum NonLinearConjugateGradientOptimizer.Formula

Class Inheritance

extends Enum<NonLinearConjugateGradientOptimizer.Formula>

java.lang.Object
java.lang.Enum
org.apache.commons.math3.optim.nonlinear.scalar.gradient.NonLinearConjugateGradientOptimizer.Formula

Available choices of update formulas for the updating the parameter that is used to compute the successive conjugate search directions. For non-linear conjugate gradients, there are two formulas:

Fletcher-Reeves formula
Polak-Ribière formula

On the one hand, the Fletcher-Reeves formula is guaranteed to converge if the start point is close enough of the optimum whether the Polak-Ribière formula may not converge in rare cases. On the other hand, the Polak-Ribière formula is often faster when it does converge. Polak-Ribière is often used.

Since: 2.0

Field Summary

Modifier and Type	Field and Description
public static final NonLinearConjugateGradientOptimizer.Formula	FLETCHER_REEVES Fletcher-Reeves formula.
public static final NonLinearConjugateGradientOptimizer.Formula	POLAK_RIBIERE Polak-Ribière formula.

Constructor Summary

Access	Constructor and Description
private	Formula()

Method Summary

Modifier and Type	Method and Description
public static NonLinearConjugateGradientOptimizer.Formula	valueOf(String name)
public static NonLinearConjugateGradientOptimizer.Formula[]	values()

Inherited from java.lang.Enum:: clone compareTo describeConstable equals finalize getDeclaringClass hashCode name ordinal toString valueOf

Field Detail

FLETCHER_REEVES	back to summary
public static final NonLinearConjugateGradientOptimizer.Formula FLETCHER_REEVES Fletcher-Reeves formula.

POLAK_RIBIERE	back to summary
public static final NonLinearConjugateGradientOptimizer.Formula POLAK_RIBIERE Polak-Ribière formula.

Constructor Detail

Formula	back to summary
private Formula()

Method Detail

valueOf	back to summary
public static NonLinearConjugateGradientOptimizer.Formula valueOf(String name)

values	back to summary
public static NonLinearConjugateGradientOptimizer.Formula[] values()

org.apache.commons.math3.optim.nonlinear.scalar.gradient back to summary

public Class NonLinearConjugateGradientOptimizer.IdentityPreconditioner

Class Inheritance

extends Object
implements Preconditioner

java.lang.Object
org.apache.commons.math3.optim.nonlinear.scalar.gradient.NonLinearConjugateGradientOptimizer.IdentityPreconditioner

All Implemented Interfaces

org.apache.commons.math3.optim.nonlinear.scalar.gradient.Preconditioner

Default identity preconditioner.

Constructor Summary

Access	Constructor and Description
public	IdentityPreconditioner()

Method Summary

Modifier and Type	Method and Description
public double[]	precondition(double[] current point at which the search direction was computed variables, double[] raw search direction (i.e. opposite of the gradient) r) Implements org.apache.commons.math3.optim.nonlinear.scalar.gradient.Preconditioner.precondition. Precondition a search direction.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Constructor Detail

IdentityPreconditioner	back to summary
public IdentityPreconditioner()

Method Detail

precondition	back to summary
public double[] precondition(double[] variables, double[] r) Implements org.apache.commons.math3.optim.nonlinear.scalar.gradient.Preconditioner.precondition. Doc from org.apache.commons.math3.optim.nonlinear.scalar.gradient.Preconditioner.precondition. Precondition a search direction. The returned preconditioned search direction must be computed fast or the algorithm performances will drop drastically. A classical approach is to compute only the diagonal elements of the hessian and to divide the raw search direction by these elements if they are all positive. If at least one of them is negative, it is safer to return a clone of the raw search direction as if the hessian was the identity matrix. The rationale for this simplified choice is that a negative diagonal element means the current point is far from the optimum and preconditioning will not be efficient anyway in this case. Parameters variables:double[] current point at which the search direction was computed r:double[] raw search direction (i.e. opposite of the gradient) Returns:double[] approximation of H^-1r where H is the objective function hessian

precondition

back to summary

public double[] precondition(double[] variables, double[] r)

Implements org.apache.commons.math3.optim.nonlinear.scalar.gradient.Preconditioner.precondition.

Doc from org.apache.commons.math3.optim.nonlinear.scalar.gradient.Preconditioner.precondition.

Precondition a search direction.

The returned preconditioned search direction must be computed fast or the algorithm performances will drop drastically. A classical approach is to compute only the diagonal elements of the hessian and to divide the raw search direction by these elements if they are all positive. If at least one of them is negative, it is safer to return a clone of the raw search direction as if the hessian was the identity matrix. The rationale for this simplified choice is that a negative diagonal element means the current point is far from the optimum and preconditioning will not be efficient anyway in this case.

Parameters

variables:double[]: current point at which the search direction was computed
r:double[]: raw search direction (i.e. opposite of the gradient)

Returns:double[]

approximation of H^-1r where H is the objective function hessian

public Class NonLinearConjugateGradientOptimizer

Nested and Inner Type Summary

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

public Class NonLinearConjugateGradientOptimizer.BracketingStep

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

public final Enum NonLinearConjugateGradientOptimizer.Formula

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

public Class NonLinearConjugateGradientOptimizer.IdentityPreconditioner

Constructor Summary

Method Summary

Constructor Detail

Method Detail