org.drip.optimization.constrained

Class OptimizationFramework

java.lang.Object

org.drip.function.definition.RdToR1

org.drip.optimization.constrained.OptimizationFramework

public class OptimizationFramework
extends RdToR1

OptimizationFramework holds the Non Linear Objective Function and the Collection of Equality and the Inequality Constraints that correspond to the Optimization Setup. 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, Technical Report, Federal University of Parana. - Karush, A. (1939): Minima of Functions of Several Variables with Inequalities as Side Constraints, M. Sc., 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.

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor and Description
OptimizationFramework(RdToR1 rdToR1Objective, RdToR1[] aRdToR1EqualityConstraint, RdToR1[] aRdToR1InequalityConstraint) OptimizationFramework Constructor

Method Summary

Modifier and Type	Method and Description
boolean	activeConstraintLinearDependence(double[] adblVariate, boolean bPositiveLinearDependenceCheck) Active Constraint Set Linear Dependence Check
int	activeConstraintRank(double[] adblVariate) Active Constraint Set Rank Computation
boolean	activeConstraintRankComparison(double[] adblVariate, int iRank) Compare the Active Constraint Set Rank at the specified against the specified Rank
RdToR1[]	activeConstraints(double[] adblVariate) Retrieve the Array of Active Constraints
double[][]	alongAwayVariate(double[] adblVariate) Compute the Along/Away "Naturally" Incremented Variates
boolean	complementarySlacknessCheck(FritzJohnMultipliers fjm, double[] adblVariate) Check for Complementary Slackness across the Inequality Constraints
int	constraintFunctionDimension() Retrieve the Constraint Function Dimension
int	dimension() Retrieve the Dimension of the Input Variate
RdToR1[]	equalityConstraint() Retrieve the Array of R^d To R^1 Equality Constraint Functions
double	evaluate(double[] adblVariate) Evaluate for the given Input Variates
double[][]	hessian(double[] adblVariate) Evaluate The Hessian for the given Input Variates
RdToR1[]	inequalityConstraint() Retrieve the Array of R^d To R^1 Inequality Constraint Functions
boolean	isCompatible(FritzJohnMultipliers fjm) Indicate if the specified Fritz John Multipliers are compatible with the Optimization Framework
boolean	isCPLDCQ(double[] adblVariate) Check for Constant Positive Linear Dependence Constraint Qualification
boolean	isCRCQ(double[] adblVariate) Check for Constant Rank Constraint Qualification
boolean	isFONC(FritzJohnMultipliers fjm, double[] adblVariate) Check the Candidate Point for First Order Necessary Condition
boolean	isLagrangian() Indicate if the Optimizer Framework is Lagrangian
boolean	isLCQ() Check for Linearity Constraint Qualification
boolean	isLICQ(double[] adblVariate) Check for Linearity Independent Constraint Qualification
boolean	isMFCQ(double[] adblVariate) Check for Mangasarian Fromovitz Constraint Qualification
boolean	isQNCQ(FritzJohnMultipliers fjm, double[] adblVariate) Check for Quasi Normal Constraint Qualification
boolean	isSCCQ(double[] adblVariate) Check for Slater Condition Constraint Qualification
boolean	isSOSC(FritzJohnMultipliers fjm, double[] adblVariate, boolean bCheckForMinima) Check the Candidate Point for Second Order Sufficiency Condition
boolean	isUnconstrained() Indicate if the Optimizer Framework is Unconstrained
double[]	jacobian(double[] adblVariate) Evaluate the Jacobian for the given Input Variates
NecessarySufficientConditions	necessarySufficientQualifier(FritzJohnMultipliers fjm, double[] adblVariate, boolean bCheckForMinima) Generate the Battery of Necessary and Sufficient Qualification Tests
int	numEqualityConstraint() Retrieve the Number of Equality Constraints
int	numInequalityConstraint() Retrieve the Number of Inequality Constraints
RdToR1	objectiveFunction() Retrieve the R^d To R^1 Objective Function
int	objectiveFunctionDimension() Retrieve the Objective Function Dimension
boolean	primalFeasibilityCheck(double[] adblVariate) Check the Candidate Point for Primal Feasibility
RegularityConditions	regularityQualifier(FritzJohnMultipliers fjm, double[] adblVariate) Generate the Battery of Regularity Constraint Qualification Tests

Methods inherited from class org.drip.function.definition.RdToR1

derivative, differential, gradient, gradientModulus, gradientModulusFunction, integrate, maxima, minima, ValidateInput

Methods inherited from class java.lang.Object

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

Constructor Detail

OptimizationFramework

public OptimizationFramework(RdToR1 rdToR1Objective,
                             RdToR1[] aRdToR1EqualityConstraint,
                             RdToR1[] aRdToR1InequalityConstraint)
                      throws java.lang.Exception

OptimizationFramework Constructor

Parameters:

rdToR1Objective - The R^d To R^1 Objective Function

aRdToR1EqualityConstraint - The Array of R^d To R^1 Equality Constraint Functions

aRdToR1InequalityConstraint - The Array of R^d To R^1 Inequality Constraint Functions

Throws:

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

Method Detail

objectiveFunction

public RdToR1 objectiveFunction()

Retrieve the R^d To R^1 Objective Function

Returns:

The R^d To R^1 Objective Function

equalityConstraint

public RdToR1[] equalityConstraint()

Retrieve the Array of R^d To R^1 Equality Constraint Functions

Returns:

The Array of R^d To R^1 Equality Constraint Functions

inequalityConstraint

public RdToR1[] inequalityConstraint()

Retrieve the Array of R^d To R^1 Inequality Constraint Functions

Returns:

The Array of R^d To R^1 Inequality Constraint Functions

numEqualityConstraint

public int numEqualityConstraint()

Retrieve the Number of Equality Constraints

Returns:

The Number of Equality Constraints

numInequalityConstraint

public int numInequalityConstraint()

Retrieve the Number of Inequality Constraints

Returns:

The Number of Inequality Constraints

isLagrangian

public boolean isLagrangian()

Indicate if the Optimizer Framework is Lagrangian

Returns:

TRUE - The Optimizer Framework is Lagrangian

isUnconstrained

public boolean isUnconstrained()

Indicate if the Optimizer Framework is Unconstrained

Returns:

TRUE - The Optimizer Framework is Unconstrained

isCompatible

public boolean isCompatible(FritzJohnMultipliers fjm)

Indicate if the specified Fritz John Multipliers are compatible with the Optimization Framework

Parameters:

fjm - The specified FJM Multipliers

Returns:

TRUE - The specified Fritz John Multipliers are compatible with the Optimization Framework

primalFeasibilityCheck

public boolean primalFeasibilityCheck(double[] adblVariate)
                               throws java.lang.Exception

Check the Candidate Point for Primal Feasibility

Parameters:

adblVariate - The Candidate R^d Variate

Returns:

TRUE - The Candidate Point has passed the Primal Feasibility Test

Throws:

java.lang.Exception - Thrown if the Input in Invalid

complementarySlacknessCheck

public boolean complementarySlacknessCheck(FritzJohnMultipliers fjm,
                                           double[] adblVariate)
                                    throws java.lang.Exception

Check for Complementary Slackness across the Inequality Constraints

Parameters:

fjm - The specified Fritz John Multipliers

adblVariate - The Candidate R^d Variate

Returns:

TRUE - The Complementary Slackness Test passed

Throws:

java.lang.Exception - Thrown if the Input in Invalid

isFONC

public boolean isFONC(FritzJohnMultipliers fjm,
                      double[] adblVariate)
               throws java.lang.Exception

Check the Candidate Point for First Order Necessary Condition

Parameters:

fjm - The specified Fritz John Multipliers

adblVariate - The Candidate R^d Variate

Returns:

TRUE - The Candidate Point satisfied the First Order Necessary Condition

Throws:

java.lang.Exception - Thrown if the Input in Invalid

isSOSC

public boolean isSOSC(FritzJohnMultipliers fjm,
                      double[] adblVariate,
                      boolean bCheckForMinima)
               throws java.lang.Exception

Check the Candidate Point for Second Order Sufficiency Condition

Parameters:

fjm - The specified Fritz John Multipliers

adblVariate - The Candidate R^d Variate

bCheckForMinima - TRUE - Check whether the R^d Variate corresponds to the SOSC Minimum

Returns:

TRUE - The Candidate Point satisfies the Second Order Sufficiency Condition

Throws:

java.lang.Exception - Thrown if the Input in Invalid

necessarySufficientQualifier

public NecessarySufficientConditions necessarySufficientQualifier(FritzJohnMultipliers fjm,
                                                                  double[] adblVariate,
                                                                  boolean bCheckForMinima)

Generate the Battery of Necessary and Sufficient Qualification Tests

Parameters:

fjm - The specified Fritz John Multipliers

adblVariate - The Candidate R^d Variate

bCheckForMinima - TRUE - Check whether the R^d Variate corresponds to the SOSC Minimum

Returns:

The Necessary and Sufficient Conditions Qualifier Instance

activeConstraints

public RdToR1[] activeConstraints(double[] adblVariate)

Retrieve the Array of Active Constraints

Parameters:

adblVariate - The R^d Variate

Returns:

The Array of Active Constraints

activeConstraintRank

public int activeConstraintRank(double[] adblVariate)
                         throws java.lang.Exception

Active Constraint Set Rank Computation

Parameters:

adblVariate - The Candidate R^d Variate

Returns:

The Active Constraint Set Rank

Throws:

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

activeConstraintRankComparison

public boolean activeConstraintRankComparison(double[] adblVariate,
                                              int iRank)
                                       throws java.lang.Exception

Compare the Active Constraint Set Rank at the specified against the specified Rank

Parameters:

adblVariate - The Candidate R^d Variate

iRank - The specified Rank

Returns:

TRUE - Active Constraint Set Rank matches the specified Rank

Throws:

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

activeConstraintLinearDependence

public boolean activeConstraintLinearDependence(double[] adblVariate,
                                                boolean bPositiveLinearDependenceCheck)
                                         throws java.lang.Exception

Active Constraint Set Linear Dependence Check

Parameters:

adblVariate - The Candidate R^d Variate

bPositiveLinearDependenceCheck - TRUE - Perform an Additional Positive Dependence Check

Returns:

TRUE - Active Constraint Set Linear Dependence Check is satisfied

Throws:

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

alongAwayVariate

public double[][] alongAwayVariate(double[] adblVariate)

Compute the Along/Away "Naturally" Incremented Variates

Parameters:

adblVariate - The Candidate R^d Variate

Returns:

The Along/Away "Natural" Incremented Variates

isLCQ

public boolean isLCQ()

Check for Linearity Constraint Qualification

Returns:

TRUE - Linearity Constraint Qualification is satisfied

isLICQ

public boolean isLICQ(double[] adblVariate)
               throws java.lang.Exception

Check for Linearity Independent Constraint Qualification

Parameters:

adblVariate - The Candidate R^d Variate

Returns:

TRUE - Linearity Independent Constraint Qualification is satisfied

Throws:

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

isMFCQ

public boolean isMFCQ(double[] adblVariate)
               throws java.lang.Exception

Check for Mangasarian Fromovitz Constraint Qualification

Parameters:

adblVariate - The Candidate R^d Variate

Returns:

TRUE - The Mangasarian Fromovitz Constraint Qualification is satisfied

Throws:

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

isCRCQ

public boolean isCRCQ(double[] adblVariate)
               throws java.lang.Exception

Check for Constant Rank Constraint Qualification

Parameters:

adblVariate - The Candidate R^d Variate

Returns:

TRUE - The Constant Rank Constraint Qualification is satisfied

Throws:

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

isCPLDCQ

public boolean isCPLDCQ(double[] adblVariate)
                 throws java.lang.Exception

Check for Constant Positive Linear Dependence Constraint Qualification

Parameters:

adblVariate - The Candidate R^d Variate

Returns:

TRUE - The Constant Positive Linear Dependence Constraint Qualification is satisfied

Throws:

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

isQNCQ

public boolean isQNCQ(FritzJohnMultipliers fjm,
                      double[] adblVariate)
               throws java.lang.Exception

Check for Quasi Normal Constraint Qualification

Parameters:

fjm - The specified Fritz John Multipliers

adblVariate - The Candidate R^d Variate

Returns:

TRUE - The Quasi Normal Constraint Qualification is satisfied

Throws:

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

isSCCQ

public boolean isSCCQ(double[] adblVariate)
               throws java.lang.Exception

Check for Slater Condition Constraint Qualification

Parameters:

adblVariate - The Candidate R^d Variate

Returns:

TRUE - The Slater Condition Constraint Qualification is satisfied

Throws:

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

regularityQualifier

public RegularityConditions regularityQualifier(FritzJohnMultipliers fjm,
                                                double[] adblVariate)

Generate the Battery of Regularity Constraint Qualification Tests

Parameters:

fjm - The specified Fritz John Multipliers

adblVariate - The Candidate R^d Variate

Returns:

The Regularity Constraint Qualifier Instance

objectiveFunctionDimension

public int objectiveFunctionDimension()

Retrieve the Objective Function Dimension

Returns:

The Objective Function Dimension

constraintFunctionDimension

public int constraintFunctionDimension()

Retrieve the Constraint Function Dimension

Returns:

The Constraint Function Dimension

dimension

public int dimension()

Description copied from class: RdToR1

Retrieve the Dimension of the Input Variate

Specified by:

dimension in class RdToR1

Returns:

The Dimension of the Input Variate

evaluate

public double evaluate(double[] adblVariate)
                throws java.lang.Exception

Description copied from class: RdToR1

Evaluate for the given Input Variates

Specified by:

evaluate in class RdToR1

Parameters:

adblVariate - Array of Input Variates

Returns:

The Calculated Value

Throws:

java.lang.Exception - Thrown if the Evaluation cannot be done

jacobian

public double[] jacobian(double[] adblVariate)

Description copied from class: RdToR1

Evaluate the Jacobian for the given Input Variates

Overrides:

jacobian in class RdToR1

Parameters:

adblVariate - Array of Input Variates

Returns:

The Jacobian Array

hessian

public double[][] hessian(double[] adblVariate)

Description copied from class: RdToR1

Evaluate The Hessian for the given Input Variates

Overrides:

hessian in class RdToR1

Parameters:

adblVariate - Array of Input Variates

Returns:

The Hessian Matrix