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. 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[] adblVariate, FritzJohnMultipliers fjm, ConstraintQualifierLCQ cqLCQ, ConstraintQualifierLICQ cqLICQ, ConstraintQualifierMFCQ cqMFCQ, ConstraintQualifierCRCQ cqCRCQ, ConstraintQualifierCPLDCQ cqCPLDCQ, ConstraintQualifierQNCQ cqQNCQ, ConstraintQualifierSCCQ cqSCCQ)	RegularityConditions Constructor

Method Summary

Modifier and Type	Method	Description
ConstraintQualifierCPLDCQ	cpldcq()	Retrieve the CPLDCQ Constraint Qualifier
ConstraintQualifierCRCQ	crcq()	Retrieve the CRCQ Constraint Qualifier
FritzJohnMultipliers	fjm()	Retrieve the Fritz John Mutipliers
ConstraintQualifierLCQ	lcq()	Retrieve the LCQ Constraint Qualifier
ConstraintQualifierLICQ	licq()	Retrieve the LICQ Constraint Qualifier
ConstraintQualifierMFCQ	mfcq()	Retrieve the MFCQ Constraint Qualifier
ConstraintQualifierQNCQ	qncq()	Retrieve the QNCQ Constraint Qualifier
ConstraintQualifierSCCQ	sccq()	Retrieve the SCCQ Constraint Qualifier
static RegularityConditions	Standard(double[] adblVariate, FritzJohnMultipliers fjm, boolean bValidLCQ, boolean bValidLICQ, boolean bValidMFCQ, boolean bValidCRCQ, boolean bValidCPLDCQ, boolean bValidQNCQ, boolean bValidSCCQ)	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[]	variate()	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[] adblVariate,
FritzJohnMultipliers fjm,
ConstraintQualifierLCQ cqLCQ,
ConstraintQualifierLICQ cqLICQ,
ConstraintQualifierMFCQ cqMFCQ,
ConstraintQualifierCRCQ cqCRCQ,
ConstraintQualifierCPLDCQ cqCPLDCQ,
ConstraintQualifierQNCQ cqQNCQ,
ConstraintQualifierSCCQ cqSCCQ)
                     throws java.lang.Exception

RegularityConditions Constructor

Parameters:

adblVariate - The Candidate Variate Array

fjm - The Fritz John Multipliers

cqLCQ - LCQ Constraint Qualifier Instance

cqLICQ - LICQ Constraint Qualifier Instance

cqMFCQ - MFCQ Constraint Qualifier Instance

cqCRCQ - CRCQ Constraint Qualifier Instance

cqCPLDCQ - CPLDCQ Constraint Qualifier Instance

cqQNCQ - QNCQ Constraint Qualifier Instance

cqSCCQ - SCCQ Constraint Qualifier Instance

Throws:

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

Method Details

Standard

public static final RegularityConditions Standard(double[] adblVariate,
FritzJohnMultipliers fjm,
boolean bValidLCQ,
boolean bValidLICQ,
boolean bValidMFCQ,
boolean bValidCRCQ,
boolean bValidCPLDCQ,
boolean bValidQNCQ,
boolean bValidSCCQ)

Construct a Standard Instance of RegularityConditions

Parameters:

adblVariate - The Candidate Variate Array

fjm - The Fritz John Multipliers

bValidLCQ - The LCQ Validity Flag

bValidLICQ - The LICQ Validity Flag

bValidMFCQ - The MFCQ Validity Flag

bValidCRCQ - The CRCQ Validity Flag

bValidCPLDCQ - The CPLDCQ Validity Flag

bValidQNCQ - The QNCQ Validity Flag

bValidSCCQ - The SCCQ Validity Flag

Returns:

The Standard Instance of CandidateRegularity

variate

public double[] variate()

Retrieve the Candidate Variate Array

Returns:

The Candidate Variate Array

fjm

public FritzJohnMultipliers fjm()

Retrieve the Fritz John Mutipliers

Returns:

The Fritz John Mutipliers

lcq

public ConstraintQualifierLCQ lcq()

Retrieve the LCQ Constraint Qualifier

Returns:

The LCQ Constraint Qualifier

licq

public ConstraintQualifierLICQ licq()

Retrieve the LICQ Constraint Qualifier

Returns:

The LICQ Constraint Qualifier

mfcq

public ConstraintQualifierMFCQ mfcq()

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)