gov.sandia.cognition.learning.algorithm.minimization

Class FunctionMinimizerConjugateGradient

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.algorithm.AbstractIterativeAlgorithm

gov.sandia.cognition.algorithm.AbstractAnytimeAlgorithm<ResultType>

gov.sandia.cognition.learning.algorithm.AbstractAnytimeBatchLearner<EvaluatorType,InputOutputPair<InputType,OutputType>>

gov.sandia.cognition.learning.algorithm.minimization.AbstractAnytimeFunctionMinimizer<Vector,java.lang.Double,DifferentiableEvaluator<? super Vector,java.lang.Double,Vector>>

gov.sandia.cognition.learning.algorithm.minimization.FunctionMinimizerConjugateGradient

All Implemented Interfaces:

AnytimeAlgorithm<InputOutputPair<Vector,java.lang.Double>>, IterativeAlgorithm, StoppableAlgorithm, AnytimeBatchLearner<DifferentiableEvaluator<? super Vector,java.lang.Double,Vector>,InputOutputPair<Vector,java.lang.Double>>, BatchLearner<DifferentiableEvaluator<? super Vector,java.lang.Double,Vector>,InputOutputPair<Vector,java.lang.Double>>, FunctionMinimizer<Vector,java.lang.Double,DifferentiableEvaluator<? super Vector,java.lang.Double,Vector>>, CloneableSerializable, java.io.Serializable, java.lang.Cloneable

Direct Known Subclasses:

FunctionMinimizerFletcherReeves, FunctionMinimizerLiuStorey, FunctionMinimizerPolakRibiere

@PublicationReference(author="R. Fletcher",title="Practical Methods of Optimization, Second Edition",type=Book,year=1987,pages={80,87},notes="Section 4.1") @PublicationReference(author="Wikipedia",title="Nonlinear conjugate gradient method",type=WebPage,url="http://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method",year=2008) @PublicationReference(author={"William H. Press","Saul A. Teukolsky","William T. Vetterling","Brian P. Flannery"},title="Numerical Recipes in C, Second Edition",type=Book,year=1992,pages={423,424},notes="Section 10.6",url="http://www.nrbook.com/a/bookcpdf.php")
public abstract class FunctionMinimizerConjugateGradient
extends AbstractAnytimeFunctionMinimizer<Vector,java.lang.Double,DifferentiableEvaluator<? super Vector,java.lang.Double,Vector>>

Conjugate gradient method is a class of algorithms for finding the unconstrained local minimum of a nonlinear function. CG algorithms find the local minimum by using a line search algorithm along a "conjugate gradient" direction using first-order (gradient) information. The particular approaches vary only slightly according to how the direction is updated. However, in my experience, the Liu-Storey CG variant (FunctionMinimizerLiuStorey) performs the best.

All CG variants tend to require more function/gradient evaluations than their Quasi-Newton cousins. However, CG methods only require O(N) storage, whereas Quasi-Newton algorithms (FunctionMinimizerQuasiNewton) require O(N*N) storage, where N is the size of the input space. So, if your input space is large, then CG algorithms may be the method of choice. In any case, the Liu-Storey CG variant tends to perform fairly well compared to the best Quasi-Newton algorithms, BFGS in particular.

Since:

2.1

Author:

Kevin R. Dixon

See Also:

FunctionMinimizerQuasiNewton, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static LineMinimizer<?>	DEFAULT_LINE_MINIMIZER Default line minimization algorithm, LineMinimizerDerivativeBased
static int	DEFAULT_MAX_ITERATIONS Default maximum number of iterations before stopping, 1000
static double	DEFAULT_TOLERANCE Default tolerance, 1.0E-5
protected DirectionalVectorToDifferentiableScalarFunction	lineFunction Function that maps a Evaluator onto a Evaluator using a set point, direction and scale factor

Fields inherited from class gov.sandia.cognition.learning.algorithm.minimization.AbstractAnytimeFunctionMinimizer

initialGuess, result, tolerance

Fields inherited from class gov.sandia.cognition.learning.algorithm.AbstractAnytimeBatchLearner

data, keepGoing

Fields inherited from class gov.sandia.cognition.algorithm.AbstractAnytimeAlgorithm

maxIterations

Fields inherited from class gov.sandia.cognition.algorithm.AbstractIterativeAlgorithm

DEFAULT_ITERATION, iteration

Constructor Summary

Constructors

Constructor and Description
FunctionMinimizerConjugateGradient(LineMinimizer<?> lineMinimizer, Vector initialGuess, double tolerance, int maxIterations) Creates a new instance of FunctionMinimizerConjugateGradient

Method Summary

Modifier and Type	Method and Description
protected void	cleanupAlgorithm() Called to clean up the learning algorithm's state after learning has finished.
protected abstract double	computeScaleFactor(Vector gradientCurrent, Vector gradientPrevious) Computes the conjugate gradient parameter for the particular update scheme.
LineMinimizer<?>	getLineMinimizer() Getter for lineMinimizer
protected boolean	initializeAlgorithm() Called to initialize the learning algorithm's state based on the data that is stored in the data field.
void	setLineMinimizer(LineMinimizer<?> lineMinimizer) Setter for lineMinimizer
protected boolean	step() Called to take a single step of the learning algorithm.

Methods inherited from class gov.sandia.cognition.learning.algorithm.minimization.AbstractAnytimeFunctionMinimizer

getInitialGuess, getResult, getTolerance, setInitialGuess, setResult, setTolerance

Methods inherited from class gov.sandia.cognition.learning.algorithm.AbstractAnytimeBatchLearner

clone, getData, getKeepGoing, learn, setData, setKeepGoing, stop

Methods inherited from class gov.sandia.cognition.algorithm.AbstractAnytimeAlgorithm

getMaxIterations, isResultValid, setMaxIterations

Methods inherited from class gov.sandia.cognition.algorithm.AbstractIterativeAlgorithm

addIterativeAlgorithmListener, fireAlgorithmEnded, fireAlgorithmStarted, fireStepEnded, fireStepStarted, getIteration, getListeners, removeIterativeAlgorithmListener, setIteration, setListeners

Methods inherited from class java.lang.Object

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

Methods inherited from interface gov.sandia.cognition.learning.algorithm.minimization.FunctionMinimizer

learn

Methods inherited from interface gov.sandia.cognition.util.CloneableSerializable

clone

Methods inherited from interface gov.sandia.cognition.algorithm.AnytimeAlgorithm

getMaxIterations, setMaxIterations

Methods inherited from interface gov.sandia.cognition.algorithm.IterativeAlgorithm

addIterativeAlgorithmListener, getIteration, removeIterativeAlgorithmListener

Methods inherited from interface gov.sandia.cognition.algorithm.StoppableAlgorithm

isResultValid, stop

Field Detail

DEFAULT_MAX_ITERATIONS

public static final int DEFAULT_MAX_ITERATIONS

Default maximum number of iterations before stopping, 1000

See Also:

Constant Field Values

DEFAULT_TOLERANCE

public static final double DEFAULT_TOLERANCE

Default tolerance, 1.0E-5

See Also:

Constant Field Values

DEFAULT_LINE_MINIMIZER

public static final LineMinimizer<?> DEFAULT_LINE_MINIMIZER

Default line minimization algorithm, LineMinimizerDerivativeBased

lineFunction

protected DirectionalVectorToDifferentiableScalarFunction lineFunction

Function that maps a Evaluator onto a Evaluator using a set point, direction and scale factor

Constructor Detail

FunctionMinimizerConjugateGradient

public FunctionMinimizerConjugateGradient(LineMinimizer<?> lineMinimizer,
                                          Vector initialGuess,
                                          double tolerance,
                                          int maxIterations)

Creates a new instance of FunctionMinimizerConjugateGradient

Parameters:

initialGuess - Initial guess about the minimum of the method

tolerance - Tolerance of the minimization algorithm, must be >= 0.0, typically ~1e-10

lineMinimizer - Work-horse algorithm that minimizes the function along a direction

maxIterations - Maximum number of iterations, must be >0, typically ~100

Method Detail

getLineMinimizer

public LineMinimizer<?> getLineMinimizer()

Getter for lineMinimizer

Returns:

Work-horse algorithm that minimizes the function along a direction

setLineMinimizer

public void setLineMinimizer(LineMinimizer<?> lineMinimizer)

Setter for lineMinimizer

Parameters:

lineMinimizer - Work-horse algorithm that minimizes the function along a direction

initializeAlgorithm

protected boolean initializeAlgorithm()

Description copied from class: AbstractAnytimeBatchLearner

Called to initialize the learning algorithm's state based on the data that is stored in the data field. The return value indicates if the algorithm can be run or not based on the initialization.

Specified by:

initializeAlgorithm in class AbstractAnytimeBatchLearner<DifferentiableEvaluator<? super Vector,java.lang.Double,Vector>,InputOutputPair<Vector,java.lang.Double>>

Returns:

True if the learning algorithm can be run and false if it cannot.

step

protected boolean step()

Description copied from class: AbstractAnytimeBatchLearner

Called to take a single step of the learning algorithm.

Specified by:

step in class AbstractAnytimeBatchLearner<DifferentiableEvaluator<? super Vector,java.lang.Double,Vector>,InputOutputPair<Vector,java.lang.Double>>

Returns:

True if another step can be taken and false it the algorithm should halt.

cleanupAlgorithm

protected void cleanupAlgorithm()

Description copied from class: AbstractAnytimeBatchLearner

Called to clean up the learning algorithm's state after learning has finished.

Specified by:

cleanupAlgorithm in class AbstractAnytimeBatchLearner<DifferentiableEvaluator<? super Vector,java.lang.Double,Vector>,InputOutputPair<Vector,java.lang.Double>>

computeScaleFactor

protected abstract double computeScaleFactor(Vector gradientCurrent,
                                             Vector gradientPrevious)

Computes the conjugate gradient parameter for the particular update scheme.

Parameters:

gradientCurrent - Gradient at the current evaluation point

gradientPrevious - Gradient at the previous evaluation point

Returns:

"beta" scale factor