Package org.drip.function.rdtor1descent

Class CurvatureEvolutionVerifier

java.lang.Object

org.drip.function.rdtor1descent.LineEvolutionVerifier

org.drip.function.rdtor1descent.CurvatureEvolutionVerifier

public class CurvatureEvolutionVerifier
extends LineEvolutionVerifier

CurvatuveEvolutionVerifier implements the Armijo Criterion used for the Inexact Line Search Increment Generation to ascertain that the Gradient of the Function has reduced sufficiently. The References are:

• Wolfe, P. (1969): Convergence Conditions for Ascent Methods SIAM Review 11 (2) 226-235
• Wolfe, P. (1971): Convergence Conditions for Ascent Methods; II: Some Corrections SIAM Review 13 (2) 185-188

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = R^d To R^d Function Analysis
• Package = R^d To R¹ Gradient Descent Techniques

Author:

Lakshmi Krishnamurthy

Field Summary

Fields

Modifier and Type	Field	Description
static double	NOCEDAL_WRIGHT_CURVATURE_PARAMETER	The Nocedal-Wright Curvature Parameter

Constructor Summary

Constructors

Constructor	Description
CurvatureEvolutionVerifier(double curvatureParameter, boolean strongCurvatureCriterion)	CurvatureEvolutionVerifier Constructor

Method Summary

Modifier and Type	Method	Description
double	curvatureParameter()	Retrieve the Curvature Parameter
LineEvolutionVerifierMetrics	metrics(UnitVector targetDirectionUnitVector, double[] currentVariateArray, RdToR1 multivariateFunction, double stepLength)	Generate the Verifier Metrics for the Specified Inputs
static CurvatureEvolutionVerifier	NocedalWrightStandard(boolean strongCurvatureCriterion)	Construct the Nocedal-Wright Curvature Evolution Verifier
boolean	strongCurvatureCriterion()	Retrieve Whether of not the "Strong" Curvature Criterion needs to be met

Methods inherited from class org.drip.function.rdtor1descent.LineEvolutionVerifier

verify

Methods inherited from class java.lang.Object

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

Field Details

NOCEDAL_WRIGHT_CURVATURE_PARAMETER

public static final double NOCEDAL_WRIGHT_CURVATURE_PARAMETER

The Nocedal-Wright Curvature Parameter

See Also:

Constant Field Values

Constructor Details

CurvatureEvolutionVerifier

public CurvatureEvolutionVerifier(double curvatureParameter,
boolean strongCurvatureCriterion)
                           throws java.lang.Exception

CurvatureEvolutionVerifier Constructor

Parameters:

curvatureParameter - The Curvature Parameter

strongCurvatureCriterion - TRUE - Apply the Strong Curvature Criterion

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

NocedalWrightStandard

public static final CurvatureEvolutionVerifier NocedalWrightStandard(boolean strongCurvatureCriterion)

Construct the Nocedal-Wright Curvature Evolution Verifier

Parameters:

strongCurvatureCriterion - TRUE - Apply the Strong Curvature Criterion

Returns:

The Nocedal-Wright Curvature Evolution Verifier Instance

curvatureParameter

public double curvatureParameter()

Retrieve the Curvature Parameter

Returns:

The Curvature Parameter

strongCurvatureCriterion

public boolean strongCurvatureCriterion()

Retrieve Whether of not the "Strong" Curvature Criterion needs to be met

Returns:

TRUE - The "Strong" Curvature Criterion needs to be met

metrics

public LineEvolutionVerifierMetrics metrics(UnitVector targetDirectionUnitVector,
double[] currentVariateArray,
RdToR1 multivariateFunction,
double stepLength)

Description copied from class: LineEvolutionVerifier

Generate the Verifier Metrics for the Specified Inputs

Specified by:

metrics in class LineEvolutionVerifier

Parameters:

targetDirectionUnitVector - The Target Direction Unit Vector

currentVariateArray - The Current Variate

multivariateFunction - The R^d To R¹ Function

stepLength - The Incremental Step Length

Returns:

The Verifier Metrics