/*
* File: WolfeConditions.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Jun 6, 2008, Sandia Corporation.
* Under the terms of Contract DE-AC04-94AL85000, there is a non-exclusive
* license for use of this work by or on behalf of the U.S. Government.
* Export of this program may require a license from the United States
* Government. See CopyrightHistory.txt for complete details.
*
*/
package gov.sandia.cognition.learning.algorithm.minimization.line;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationReferences;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.learning.data.InputOutputPair;
import gov.sandia.cognition.util.AbstractCloneableSerializable;
import gov.sandia.cognition.util.ObjectUtil;
/**
* The Wolfe conditions define a set of sufficient conditions for
* "sufficient decrease" in inexact line search. These consist of two "anded"
* conditions: The Goldstein condition specifying sufficient decrease,
* sometimes called the "Armijo condition", and the curvature condition
* ensuring that a trial point is sufficiently steep. The Wolfe conditions
* are sometimes called the "Wolfe-Powell conditions".
*
* @author Kevin R. Dixon
* @since 2.1
*/
@PublicationReferences(
references={
@PublicationReference(
author="R. Fletcher",
title="Practical Methods of Optimization, Second Edition",
type=PublicationType.Book,
year=1987,
pages={26,30},
notes={
"Equation 2.5.1 and Equation 2.5.6",
"Fletcher assumes the initial point has negative slope."
}
)
,
@PublicationReference(
author="Wikipedia",
title="Wolfe conditions",
url="http://en.wikipedia.org/wiki/Wolfe_conditions",
type=PublicationType.WebPage,
year=2008
)
}
)
public class WolfeConditions
extends AbstractCloneableSerializable
{
/**
* Original point to store, slope must be less than 0.0.
*/
private InputOutputSlopeTriplet originalPoint;
/**
* Slope condition parameter for the Goldstein condition, must be less than
* curvatureCondition and on the interval (0,1).
*/
private double slopeCondition;
/**
* Curvature condition for the curvature condition, must be greater than
* slopeCondition and on the interval (0,1).
*/
private double curvatureCondition;
/**
* Creates a new instance of WolfeConditions
*
* @param originalPoint
* Original point to store, slope must be less than 0.0.
* @param slopeCondition
* Slope condition parameter for the Goldstein condition, must be less than
* curvatureCondition and on the interval (0,1).
* @param curvatureCondition
* Curvature condition for the curvature condition, must be greater than
* slopeCondition and on the interval (0,1).
*/
public WolfeConditions(
InputOutputSlopeTriplet originalPoint,
double slopeCondition,
double curvatureCondition )
{
if( slopeCondition >= curvatureCondition )
{
throw new IllegalArgumentException(
"slopeCondition must be strictly less than curvatureCondition" );
}
if( originalPoint.getSlope() >= 0.0 )
{
throw new IllegalArgumentException(
"Can only use Wolfe conditions when original slope < 0.0" );
}
this.setOriginalPoint( originalPoint );
this.setSlopeCondition( slopeCondition );
this.setCurvatureCondition( curvatureCondition );
}
/**
* Copy Constructor
* @param other WolfeConditions to copy
*/
public WolfeConditions(
WolfeConditions other )
{
this( ObjectUtil.cloneSafe(other.getOriginalPoint()),
other.getSlopeCondition(),
other.getCurvatureCondition() );
}
@Override
public WolfeConditions clone()
{
WolfeConditions clone = (WolfeConditions) super.clone();
clone.setOriginalPoint( ObjectUtil.cloneSafe( this.getOriginalPoint() ) );
return clone;
}
/**
* Evaluates if the trial point meets the Wolfe conditions
* @param trialPoint
* Trial point to consider
* @return
* True if Wolfe conditions for sufficient decrease are satisfied, false if
* either the Goldstein or strict curvature conditions are not satisfied.
*/
public boolean evaluate(
InputOutputSlopeTriplet trialPoint )
{
return this.evaluateGoldsteinCondition( trialPoint ) &&
this.evaluateStrictCurvatureCondition( trialPoint.getSlope() );
}
/**
* Evaluates the Goldstein (Armijo) conditions, which is purely a
* sufficient decrease condition.
* @param trialPoint
* Trial point to consider.
* @return
* True if the Goldstein condition is satisfied, false otherwise.
*/
public boolean evaluateGoldsteinCondition(
InputOutputPair<Double,Double> trialPoint )
{
return WolfeConditions.evaluateGoldsteinCondition(
this.getOriginalPoint(), trialPoint, this.getSlopeCondition() );
}
/**
* Evaluates the Goldstein (Armijo) conditions, which is purely a
* sufficient decrease condition.
*
* @param originalPoint
* Original point to store, slope must be less than 0.0.
* @param trialPoint
* Trial point to consider.
* @param slopeCondition
* Slope condition parameter for the Goldstein condition, must be less than
* curvatureCondition and on the interval (0,1).
* @return
* True if the Goldstein condition is satisfied, false otherwise.
*/
@PublicationReference(
author="R. Fletcher",
title="Practical Methods of Optimization, Second Edition",
type=PublicationType.Book,
year=1987,
pages=27,
notes="Equation 2.5.1"
)
public static boolean evaluateGoldsteinCondition(
InputOutputSlopeTriplet originalPoint,
InputOutputPair<Double,Double> trialPoint,
double slopeCondition )
{
double delta = trialPoint.getInput() - originalPoint.getInput();
return trialPoint.getOutput() <=
originalPoint.getOutput() + delta*slopeCondition*originalPoint.getSlope();
}
/**
* Evaluates the strict curvature condition.
* @param trialSlope
* Trial slope to consider.
* @return
* True if the strict curvature condition is satisfied, false otherwise.
*/
public boolean evaluateStrictCurvatureCondition(
double trialSlope )
{
return WolfeConditions.evaluateStrictCurvatureCondition(
this.getOriginalPoint().getSlope(), trialSlope, this.getCurvatureCondition() );
}
/**
* Evaluates the strict curvature condition.
*
* @param originalSlope
* Slope at the original point.
* @param trialSlope
* Trial slope to consider.
* @param curvatureCondition
* Curvature condition for the curvature condition, must be greater than
* slopeCondition and on the interval (0,1).
* @return
* True if the strict curvature condition is satisfied, false otherwise.
*/
@PublicationReference(
author="R. Fletcher",
title="Practical Methods of Optimization, Second Edition",
type=PublicationType.Book,
year=1987,
pages=29,
notes="Equation 2.5.6"
)
public static boolean evaluateStrictCurvatureCondition(
double originalSlope,
double trialSlope,
double curvatureCondition )
{
if( originalSlope >= 0.0 )
{
throw new IllegalArgumentException(
"Original slope must be < 0.0" );
}
// Fletcher assumes that the originalSlope is < 0.0
return Math.abs( trialSlope ) <= -curvatureCondition * originalSlope;
}
/**
* Getter for originalPoint
* @return
* Original point to store, slope must be less than 0.0.
*/
public InputOutputSlopeTriplet getOriginalPoint()
{
return this.originalPoint;
}
/**
* Setter for originalPoint
* @param originalPoint
* Original point to store, slope must be less than 0.0.
*/
public void setOriginalPoint(
InputOutputSlopeTriplet originalPoint )
{
this.originalPoint = originalPoint;
}
/**
* Getter for slopeCondition
* @return
* Slope condition parameter for the Goldstein condition, must be less than
* curvatureCondition and on the interval (0,1).
*/
public double getSlopeCondition()
{
return this.slopeCondition;
}
/**
* Setter for slopeCondition
* @param slopeCondition
* Slope condition parameter for the Goldstein condition, must be less than
* curvatureCondition and on the interval (0,1).
*/
public void setSlopeCondition(
double slopeCondition )
{
if( (slopeCondition <= 0.0) || (slopeCondition >= 1.0) )
{
throw new IllegalArgumentException(
"slopeCondition must be on the interval (0,1)" );
}
this.slopeCondition = slopeCondition;
}
/**
* Getter for curvatureCondition
* @return
* Curvature condition for the curvature condition, must be greater than
* slopeCondition and on the interval (0,1).
*/
public double getCurvatureCondition()
{
return this.curvatureCondition;
}
/**
* Setter for curvatureCondition
* @param curvatureCondition
* Curvature condition for the curvature condition, must be greater than
* slopeCondition and on the interval (0,1).
*/
public void setCurvatureCondition(
double curvatureCondition )
{
if( (curvatureCondition <= 0.0) || (curvatureCondition >= 1.0) )
{
throw new IllegalArgumentException(
"curvatureCondition must be on the interval (0,1)" );
}
this.curvatureCondition = curvatureCondition;
}
}