FritzJohnMultipliers.java
package org.drip.optimization.constrained;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
* Copyright (C) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 Lakshmi Krishnamurthy
* Copyright (C) 2016 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>FritzJohnMultipliers</i> holds the Array of the Fritz John/KKT Multipliers for the Array of the
* Equality and the Inequality Constraints, one per each Constraint. The References are:
*
* <br><br>
* <ul>
* <li>
* Boyd, S., and L. van den Berghe (2009): <i>Convex Optimization</i> <b>Cambridge University
* Press</b> Cambridge UK
* </li>
* <li>
* Eustaquio, R., E. Karas, and A. Ribeiro (2008): <i>Constraint Qualification for Nonlinear
* Programming</i> <b>Federal University of Parana</b>
* </li>
* <li>
* Karush, A. (1939): <i>Minima of Functions of Several Variables with Inequalities as Side
* Constraints</i> <b>University of Chicago</b> Chicago IL
* </li>
* <li>
* Kuhn, H. W., and A. W. Tucker (1951): Nonlinear Programming <i>Proceedings of the Second Berkeley
* Symposium</i> <b>University of California</b> Berkeley CA 481-492
* </li>
* <li>
* Ruszczynski, A. (2006): <i>Nonlinear Optimization</i> <b>Princeton University Press</b> Princeton
* NJ
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/optimization/README.md">Necessary, Sufficient, and Regularity Checks for Gradient Descent in a Constrained Optimization Setup</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/optimization/constrained/README.md">KKT Fritz-John Constrained Optimizer</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class FritzJohnMultipliers {
private double[] _adblEquality = null;
private double[] _adblInequality = null;
private double _dblObjectiveCoefficient = java.lang.Double.NaN;
/**
* Construct a Standard KarushKuhnTucker (KKT) Instance of the Fritz John Multipliers
*
* @param adblEquality Array of the Equality Constraint Coefficients
* @param adblInequality Array of the Inequality Constraint Coefficients
*
* @return The KKT Instance of Fritz John Multipliers
*/
public static final FritzJohnMultipliers KarushKuhnTucker (
final double[] adblEquality,
final double[] adblInequality)
{
try {
return new FritzJohnMultipliers (1., adblEquality, adblInequality);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* FritzJohnMultipliers Constructor
*
* @param dblObjectiveCoefficient The Objective Function Coefficient
* @param adblEquality Array of the Equality Constraint Coefficients
* @param adblInequality Array of the Inequality Constraint Coefficients
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public FritzJohnMultipliers (
final double dblObjectiveCoefficient,
final double[] adblEquality,
final double[] adblInequality)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (_dblObjectiveCoefficient = dblObjectiveCoefficient))
throw new java.lang.Exception ("FritzJohnMultipliers Constructor => Invalid Inputs");
_adblEquality = adblEquality;
_adblInequality = adblInequality;
}
/**
* Retrieve the Fritz John Objective Function Multiplier
*
* @return The Fritz John Objective Function Multiplier
*/
public double objectiveCoefficient()
{
return _dblObjectiveCoefficient;
}
/**
* Retrieve the Array of the Equality Constraint Coefficients
*
* @return The Array of the Equality Constraint Coefficients
*/
public double[] equalityConstraintCoefficient()
{
return _adblEquality;
}
/**
* Retrieve the Array of the Inequality Constraint Coefficients
*
* @return The Array of the Inequality Constraint Coefficients
*/
public double[] inequalityConstraintCoefficient()
{
return _adblInequality;
}
/**
* Retrieve the Number of Equality Multiplier Coefficients
*
* @return The Number of Equality Multiplier Coefficients
*/
public int numEqualityCoefficients()
{
return null == _adblEquality ? 0 : _adblEquality.length;
}
/**
* Retrieve the Number of Inequality Multiplier Coefficients
*
* @return The Number of Inequality Multiplier Coefficients
*/
public int numInequalityCoefficients()
{
return null == _adblInequality ? 0 : _adblInequality.length;
}
/**
* Retrieve the Number of Total KKT Multiplier Coefficients
*
* @return The Number of Total KKT Multiplier Coefficients
*/
public int numTotalCoefficients()
{
return numEqualityCoefficients() + numInequalityCoefficients();
}
/**
* Indicate of the Multipliers constitute Valid Dual Feasibility
*
* @return TRUE - The Multipliers constitute Valid Dual Feasibility
*/
public boolean dualFeasibilityCheck()
{
int iNumInequalityCoefficient = numInequalityCoefficients();
for (int i = 0; i < iNumInequalityCoefficient; ++i) {
if (0. > _adblInequality[i]) return false;
}
return true;
}
}