Package org.drip.optimization.constrained

Class NecessarySufficientConditions

java.lang.Object

org.drip.optimization.constrained.NecessarySufficientConditions

public class NecessarySufficientConditions
extends java.lang.Object

NecessarySufficientConditions holds the Results of the Verification of the Necessary and the Sufficient Conditions at the specified (possibly) Optimal Variate and the corresponding Fritz John Multiplier Suite. It provides the following Functions:

• Create a Standard Instance of NecessarySufficientConditions
• NecessarySufficientConditions Constructor
• Retrieve the Candidate Variate Array
• Retrieve the Fritz John Mutipliers
• Retrieve if the Check corresponds to Local Minima
• Retrieve the Primal Feasibility Necessary Condition
• Retrieve the Dual Feasibility Necessary Condition
• Retrieve the Complementary Slackness Necessary Condition
• Retrieve the First Order Necessary Condition
• Retrieve the Second Order Sufficiency Condition
• Indicate the Necessary/Sufficient Validity across all the Condition Qualifiers
• Retrieve the Array of Condition Orders

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

NecessarySufficientConditions(double[] candidateVariateArray, FritzJohnMultipliers fritzJohnMultipliers, boolean checkForMinima, ConditionQualifierPrimalFeasibility primalFeasibilityConditionQualifier, ConditionQualifierDualFeasibility dualFeasibilityConditionQualifier, ConditionQualifierComplementarySlackness complementarySlacknessConditionQualifier, ConditionQualifierFONC foncConditionQualifier, ConditionQualifierSOSC soscConditionQualifier)

NecessarySufficientConditions Constructor

Method Summary

Modifier and Type	Method	Description
double[]	candidateVariateArray()	Retrieve the Candidate Variate Array
boolean	checkForMinima()	Retrieve if the Check corresponds to Local Minima
ConditionQualifierComplementarySlackness	complementarySlackness()	Retrieve the Complementary Slackness Necessary Condition
java.lang.String[]	conditionOrder()	Retrieve the Array of Condition Orders
ConditionQualifierDualFeasibility	dualFeasibility()	Retrieve the Dual Feasibility Necessary Condition
ConditionQualifierFONC	fonc()	Retrieve the First Order Necessary Condition
FritzJohnMultipliers	fritzJohnMultipliers()	Retrieve the Fritz John Mutipliers
ConditionQualifierPrimalFeasibility	primalFeasibility()	Retrieve the Primal Feasibility Necessary Condition
ConditionQualifierSOSC	sosc()	Retrieve the Second Order Sufficiency Condition
static NecessarySufficientConditions	Standard(double[] candidateVariateArray, FritzJohnMultipliers fritzJohnMultipliers, boolean checkForMinima, boolean primalFeasibilityValidity, boolean dualFeasibilityValidity, boolean complementarySlacknessValidity, boolean foncValidity, boolean soscValidity)	Create a Standard Instance of NecessarySufficientConditions
boolean	valid()	Indicate the Necessary/Sufficient Validity across all the Condition Qualifiers

Methods inherited from class java.lang.Object

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

Constructor Details

NecessarySufficientConditions

public NecessarySufficientConditions(double[] candidateVariateArray,
FritzJohnMultipliers fritzJohnMultipliers,
boolean checkForMinima,
ConditionQualifierPrimalFeasibility primalFeasibilityConditionQualifier,
ConditionQualifierDualFeasibility dualFeasibilityConditionQualifier,
ConditionQualifierComplementarySlackness complementarySlacknessConditionQualifier,
ConditionQualifierFONC foncConditionQualifier,
ConditionQualifierSOSC soscConditionQualifier)
                              throws java.lang.Exception

NecessarySufficientConditions Constructor

Parameters:

candidateVariateArray - The Candidate Variate Array

fritzJohnMultipliers - The Fritz John Multipliers

checkForMinima - TRUE - Check For Minima

primalFeasibilityConditionQualifier - The Primal Feasibility Necessary Condition

dualFeasibilityConditionQualifier - The Dual Feasibility Necessary Condition

complementarySlacknessConditionQualifier - The Complementary Slackness Necessary Condition

foncConditionQualifier - The First Order Necessary Condition

soscConditionQualifier - The Second Order Sufficiency Condition

Throws:

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

Method Details

Standard

public static final NecessarySufficientConditions Standard(double[] candidateVariateArray,
FritzJohnMultipliers fritzJohnMultipliers,
boolean checkForMinima,
boolean primalFeasibilityValidity,
boolean dualFeasibilityValidity,
boolean complementarySlacknessValidity,
boolean foncValidity,
boolean soscValidity)

Create a Standard Instance of NecessarySufficientConditions

Parameters:

candidateVariateArray - The Candidate Variate Array

fritzJohnMultipliers - The Fritz John Multipliers

checkForMinima - TRUE - Check For Minima

primalFeasibilityValidity - The Primal Feasibility Validity Indicator

dualFeasibilityValidity - The Dual Feasibility Validity Indicator

complementarySlacknessValidity - The Complementary Slackness Validity Indicator

foncValidity - The FONC Validity Indicator

soscValidity - The SOSC Validity Indicator

Returns:

The Standard NecessarySufficientConditions Instance

candidateVariateArray

public double[] candidateVariateArray()

Retrieve the Candidate Variate Array

Returns:

The Candidate Variate Array

fritzJohnMultipliers

public FritzJohnMultipliers fritzJohnMultipliers()

Retrieve the Fritz John Mutipliers

Returns:

The Fritz John Mutipliers

checkForMinima

public boolean checkForMinima()

Retrieve if the Check corresponds to Local Minima

Returns:

TRUE - The Check corresponds to Local Minima

primalFeasibility

public ConditionQualifierPrimalFeasibility primalFeasibility()

Retrieve the Primal Feasibility Necessary Condition

Returns:

The Primal Feasibility Necessary Condition

dualFeasibility

public ConditionQualifierDualFeasibility dualFeasibility()

Retrieve the Dual Feasibility Necessary Condition

Returns:

The Dual Feasibility Necessary Condition

complementarySlackness

public ConditionQualifierComplementarySlackness complementarySlackness()

Retrieve the Complementary Slackness Necessary Condition

Returns:

The Complementary Slackness Necessary Condition

fonc

public ConditionQualifierFONC fonc()

Retrieve the First Order Necessary Condition

Returns:

The First Order Necessary Condition

sosc

public ConditionQualifierSOSC sosc()

Retrieve the Second Order Sufficiency Condition

Returns:

The Second Order Sufficiency Condition

valid

public boolean valid()

Indicate the Necessary/Sufficient Validity across all the Condition Qualifiers

Returns:

TRUE - The Necessary/Sufficient Criteria is satisfied across all the Condition Qualifiers

conditionOrder

public java.lang.String[] conditionOrder()

Retrieve the Array of Condition Orders

Returns:

The Array of Condition Orders