Package org.drip.optimization.constrained

Class RegularityConditions

java.lang.Object

org.drip.optimization.constrained.RegularityConditions

public class RegularityConditions
extends java.lang.Object

RegularityConditions holds the Results of the Verification of the Regularity Conditions/Constraint Qualifications at the specified (possibly) Optimal Variate and the corresponding Fritz John Multipliers. It provides the following Functions:

• Construct a Standard Instance of RegularityConditions
• RegularityConditions Constructor
• Retrieve the Fritz John Mutipliers
• Retrieve the LCQ Constraint Qualifier
• Retrieve the LICQ Constraint Qualifier
• Retrieve the MFCQ Constraint Qualifier
• Retrieve the CRCQ Constraint Qualifier
• Retrieve the CPLDCQ Constraint Qualifier
• Retrieve the QNCQ Constraint Qualifier
• Retrieve the SCCQ Constraint Qualifier
• Indicate the Ordered Gross Regularity Validity across all the Constraint Qualifiers

The References are:

• Boyd, S., and L. van den Berghe (2009): Convex Optimization Cambridge University Press Cambridge UK
• Eustaquio, R., E. Karas, and A. Ribeiro (2008): Constraint Qualification for Nonlinear Programming Federal University of Parana
• Karush, A. (1939): Minima of Functions of Several Variables with Inequalities as Side Constraints University of Chicago Chicago IL
• Kuhn, H. W., and A. W. Tucker (1951): Nonlinear Programming Proceedings of the Second Berkeley Symposium University of California Berkeley CA 481-492
• Ruszczynski, A. (2006): Nonlinear Optimization Princeton University Press Princeton NJ

Module	Computational Core Module
Library	Numerical Optimizer Library
Project	Necessary, Sufficient, and Regularity Checks for Gradient Descent and LP/MILP/MINLP Schemes
Package	KKT Fritz-John Constrained Optimizer

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor

Description

RegularityConditions(double[] variateArray, FritzJohnMultipliers fritzJohnMultipliers, ConstraintQualifierLCQ lcqConstraintQualifier, ConstraintQualifierLICQ licqConstraintQualifier, ConstraintQualifierMFCQ mfcqConstraintQualifier, ConstraintQualifierCRCQ crcqConstraintQualifier, ConstraintQualifierCPLDCQ cpldcqConstraintQualifier, ConstraintQualifierQNCQ qncqConstraintQualifier, ConstraintQualifierSCCQ sccqConstraintQualifier)

RegularityConditions Constructor

Method Summary

Modifier and Type	Method	Description
ConstraintQualifierCPLDCQ	cpldcq()	Retrieve the CPLDCQ Constraint Qualifier
ConstraintQualifierCRCQ	crcq()	Retrieve the CRCQ Constraint Qualifier
FritzJohnMultipliers	fritzJohnMultipliers()	Retrieve the Fritz John Mutipliers Retrieve the LCQ Constraint Qualifier Retrieve the LICQ Constraint Qualifier Retrieve the MFCQ Constraint Qualifier Retrieve the CRCQ Constraint Qualifier Retrieve the CPLDCQ Constraint Qualifier Retrieve the QNCQ Constraint Qualifier Retrieve the SCCQ Constraint Qualifier Indicate the Ordered Gross Regularity Validity across all the Constraint Qualifiers Retrieve the Array of Strength Orders as specified in Eustaquio, Karas, and Ribeiro (2008)
ConstraintQualifierLCQ	lcqConstraintQualifier()	Retrieve the LCQ Constraint Qualifier
ConstraintQualifierLICQ	licqConstraintQualifier()	Retrieve the LICQ Constraint Qualifier
ConstraintQualifierMFCQ	mfcqConstraintQualifier()	Retrieve the MFCQ Constraint Qualifier
ConstraintQualifierQNCQ	qncq()	Retrieve the QNCQ Constraint Qualifier
ConstraintQualifierSCCQ	sccq()	Retrieve the SCCQ Constraint Qualifier
static RegularityConditions	Standard(double[] variateArray, FritzJohnMultipliers fritzJohnMultipliers, boolean validLCQ, boolean validLICQ, boolean validMFCQ, boolean validCRCQ, boolean validCPLDCQ, boolean validQNCQ, boolean validSCCQ)	Construct a Standard Instance of RegularityConditions
java.lang.String[]	strengthOrder()	Retrieve the Array of Strength Orders as specified in Eustaquio, Karas, and Ribeiro (2008)
boolean	valid()	Indicate the Ordered Gross Regularity Validity across all the Constraint Qualifiers
double[]	variateArray()	Retrieve the Candidate Variate Array

Methods inherited from class java.lang.Object

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

Constructor Details

RegularityConditions

public RegularityConditions(double[] variateArray,
FritzJohnMultipliers fritzJohnMultipliers,
ConstraintQualifierLCQ lcqConstraintQualifier,
ConstraintQualifierLICQ licqConstraintQualifier,
ConstraintQualifierMFCQ mfcqConstraintQualifier,
ConstraintQualifierCRCQ crcqConstraintQualifier,
ConstraintQualifierCPLDCQ cpldcqConstraintQualifier,
ConstraintQualifierQNCQ qncqConstraintQualifier,
ConstraintQualifierSCCQ sccqConstraintQualifier)
                     throws java.lang.Exception

RegularityConditions Constructor

Parameters:

variateArray - The Candidate Variate Array

fritzJohnMultipliers - The Fritz John Multipliers

lcqConstraintQualifier - LCQ Constraint Qualifier Instance

licqConstraintQualifier - LICQ Constraint Qualifier Instance

mfcqConstraintQualifier - MFCQ Constraint Qualifier Instance

crcqConstraintQualifier - CRCQ Constraint Qualifier Instance

cpldcqConstraintQualifier - CPLDCQ Constraint Qualifier Instance

qncqConstraintQualifier - QNCQ Constraint Qualifier Instance

sccqConstraintQualifier - SCCQ Constraint Qualifier Instance

Throws:

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

Method Details

Standard

public static final RegularityConditions Standard(double[] variateArray,
FritzJohnMultipliers fritzJohnMultipliers,
boolean validLCQ,
boolean validLICQ,
boolean validMFCQ,
boolean validCRCQ,
boolean validCPLDCQ,
boolean validQNCQ,
boolean validSCCQ)

Construct a Standard Instance of RegularityConditions

Parameters:

variateArray - The Candidate Variate Array

fritzJohnMultipliers - The Fritz John Multipliers

validLCQ - The LCQ Validity Flag

validLICQ - The LICQ Validity Flag

validMFCQ - The MFCQ Validity Flag

validCRCQ - The CRCQ Validity Flag

validCPLDCQ - The CPLDCQ Validity Flag

validQNCQ - The QNCQ Validity Flag

validSCCQ - The SCCQ Validity Flag

Returns:

The Standard Instance of RegularityConditions

variateArray

public double[] variateArray()

Retrieve the Candidate Variate Array

Returns:

The Candidate Variate Array

fritzJohnMultipliers

public FritzJohnMultipliers fritzJohnMultipliers()

Retrieve the Fritz John Mutipliers Retrieve the LCQ Constraint Qualifier Retrieve the LICQ Constraint Qualifier Retrieve the MFCQ Constraint Qualifier Retrieve the CRCQ Constraint Qualifier Retrieve the CPLDCQ Constraint Qualifier Retrieve the QNCQ Constraint Qualifier Retrieve the SCCQ Constraint Qualifier Indicate the Ordered Gross Regularity Validity across all the Constraint Qualifiers Retrieve the Array of Strength Orders as specified in Eustaquio, Karas, and Ribeiro (2008)

Returns:

The Fritz John Mutipliers

lcqConstraintQualifier

public ConstraintQualifierLCQ lcqConstraintQualifier()

Retrieve the LCQ Constraint Qualifier

Returns:

The LCQ Constraint Qualifier

licqConstraintQualifier

public ConstraintQualifierLICQ licqConstraintQualifier()

Retrieve the LICQ Constraint Qualifier

Returns:

The LICQ Constraint Qualifier

mfcqConstraintQualifier

public ConstraintQualifierMFCQ mfcqConstraintQualifier()

Retrieve the MFCQ Constraint Qualifier

Returns:

The MFCQ Constraint Qualifier

crcq

public ConstraintQualifierCRCQ crcq()

Retrieve the CRCQ Constraint Qualifier

Returns:

The CRCQ Constraint Qualifier

cpldcq

public ConstraintQualifierCPLDCQ cpldcq()

Retrieve the CPLDCQ Constraint Qualifier

Returns:

The CPLDCQ Constraint Qualifier

qncq

public ConstraintQualifierQNCQ qncq()

Retrieve the QNCQ Constraint Qualifier

Returns:

The QNCQ Constraint Qualifier

sccq

public ConstraintQualifierSCCQ sccq()

Retrieve the SCCQ Constraint Qualifier

Returns:

The SCCQ Constraint Qualifier

valid

public boolean valid()

Indicate the Ordered Gross Regularity Validity across all the Constraint Qualifiers

Returns:

TRUE - The Ordered Regularity Criteria is satisfied across all the Constraint Qualifiers

strengthOrder

public java.lang.String[] strengthOrder()

Retrieve the Array of Strength Orders as specified in Eustaquio, Karas, and Ribeiro (2008)

Returns:

The Array of Strength Orders as specified in Eustaquio, Karas, and Ribeiro (2008)