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. 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[] adblVariate, FritzJohnMultipliers fjm, boolean bCheckForMinima, ConditionQualifierPrimalFeasibility cqPrimalFeasibility, ConditionQualifierDualFeasibility cqDualFeasibility, ConditionQualifierComplementarySlackness cqComplementarySlackness, ConditionQualifierFONC cqFONC, ConditionQualifierSOSC cqSOSC)	NecessarySufficientConditions Constructor

Method Summary

Modifier and Type	Method	Description
boolean	checkFroMinima()	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[] adblVariate, FritzJohnMultipliers fjm, boolean bCheckForMinima, boolean bPrimalFeasibilityValidity, boolean bDualFeasibilityValidity, boolean bComplementarySlacknessValidity, boolean bFONCValidity, boolean bSOSCValidity)	Create a Standard Instance of NecessarySufficientConditions
boolean	valid()	Indicate the Necessary/Sufficient Validity across all the Condition 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

NecessarySufficientConditions

public NecessarySufficientConditions(double[] adblVariate,
FritzJohnMultipliers fjm,
boolean bCheckForMinima,
ConditionQualifierPrimalFeasibility cqPrimalFeasibility,
ConditionQualifierDualFeasibility cqDualFeasibility,
ConditionQualifierComplementarySlackness cqComplementarySlackness,
ConditionQualifierFONC cqFONC,
ConditionQualifierSOSC cqSOSC)
                              throws java.lang.Exception

NecessarySufficientConditions Constructor

Parameters:

adblVariate - The Candidate Variate Array

fjm - The Fritz John Multipliers

bCheckForMinima - TRUE - Check For Minima

cqPrimalFeasibility - The Primal Feasibility Necessary Condition

cqDualFeasibility - The Dual Feasibility Necessary Condition

cqComplementarySlackness - The Complementary Slackness Necessary Condition

cqFONC - The First Order Necessary Condition

cqSOSC - The Second Order Sufficiency Condition

Throws:

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

Method Details

Standard

public static final NecessarySufficientConditions Standard(double[] adblVariate,
FritzJohnMultipliers fjm,
boolean bCheckForMinima,
boolean bPrimalFeasibilityValidity,
boolean bDualFeasibilityValidity,
boolean bComplementarySlacknessValidity,
boolean bFONCValidity,
boolean bSOSCValidity)

Create a Standard Instance of NecessarySufficientConditions

Parameters:

adblVariate - The Candidate Variate Array

fjm - The Fritz John Multipliers

bCheckForMinima - TRUE - Check For Minima

bPrimalFeasibilityValidity - The Primal Feasibility Validity

bDualFeasibilityValidity - The Dual Feasibility Validity

bComplementarySlacknessValidity - The Complementary Slackness Validity

bFONCValidity - The FONC Validity

bSOSCValidity - The SOSC Validity

Returns:

The Standard NecessarySufficientConditions Instance

variate

public double[] variate()

Retrieve the Candidate Variate Array

Returns:

The Candidate Variate Array

fritzJohnMultipliers

public FritzJohnMultipliers fritzJohnMultipliers()

Retrieve the Fritz John Mutipliers

Returns:

The Fritz John Mutipliers

checkFroMinima

public boolean checkFroMinima()

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