FritzJohnMultipliers.java

  1. package org.drip.optimization.constrained;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  11.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  12.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  13.  * 
  14.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  15.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  16.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  17.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  18.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  19.  *      and computational support.
  20.  *  
  21.  *      https://lakshmidrip.github.io/DROP/
  22.  *  
  23.  *  DROP is composed of three modules:
  24.  *  
  25.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  26.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  27.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  28.  * 
  29.  *  DROP Product Core implements libraries for the following:
  30.  *  - Fixed Income Analytics
  31.  *  - Loan Analytics
  32.  *  - Transaction Cost Analytics
  33.  * 
  34.  *  DROP Portfolio Core implements libraries for the following:
  35.  *  - Asset Allocation Analytics
  36.  *  - Asset Liability Management Analytics
  37.  *  - Capital Estimation Analytics
  38.  *  - Exposure Analytics
  39.  *  - Margin Analytics
  40.  *  - XVA Analytics
  41.  * 
  42.  *  DROP Computational Core implements libraries for the following:
  43.  *  - Algorithm Support
  44.  *  - Computation Support
  45.  *  - Function Analysis
  46.  *  - Model Validation
  47.  *  - Numerical Analysis
  48.  *  - Numerical Optimizer
  49.  *  - Spline Builder
  50.  *  - Statistical Learning
  51.  * 
  52.  *  Documentation for DROP is Spread Over:
  53.  * 
  54.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  55.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  56.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  57.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  58.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  59.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  60.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  61.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  62.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  63.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  64.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  65.  * 
  66.  *  Licensed under the Apache License, Version 2.0 (the "License");
  67.  *      you may not use this file except in compliance with the License.
  68.  *   
  69.  *  You may obtain a copy of the License at
  70.  *      http://www.apache.org/licenses/LICENSE-2.0
  71.  *  
  72.  *  Unless required by applicable law or agreed to in writing, software
  73.  *      distributed under the License is distributed on an "AS IS" BASIS,
  74.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  75.  *  
  76.  *  See the License for the specific language governing permissions and
  77.  *      limitations under the License.
  78.  */

  80. /**
  81.  * <i>FritzJohnMultipliers</i> holds the Array of the Fritz John/KKT Multipliers for the Array of the
  82.  * Equality and the Inequality Constraints, one per each Constraint. The References are:
  83.  * 
  84.  * <br><br>
  85.  *  <ul>
  86.  *      <li>
  87.  *          Boyd, S., and L. van den Berghe (2009): <i>Convex Optimization</i> <b>Cambridge University
  88.  *              Press</b> Cambridge UK
  89.  *      </li>
  90.  *      <li>
  91.  *          Eustaquio, R., E. Karas, and A. Ribeiro (2008): <i>Constraint Qualification for Nonlinear
  92.  *              Programming</i> <b>Federal University of Parana</b>
  93.  *      </li>
  94.  *      <li>
  95.  *          Karush, A. (1939): <i>Minima of Functions of Several Variables with Inequalities as Side
  96.  *          Constraints</i> <b>University of Chicago</b> Chicago IL
  97.  *      </li>
  98.  *      <li>
  99.  *          Kuhn, H. W., and A. W. Tucker (1951): Nonlinear Programming <i>Proceedings of the Second Berkeley
  100.  *              Symposium</i> <b>University of California</b> Berkeley CA 481-492
  101.  *      </li>
  102.  *      <li>
  103.  *          Ruszczynski, A. (2006): <i>Nonlinear Optimization</i> <b>Princeton University Press</b> Princeton
  104.  *              NJ
  105.  *      </li>
  106.  *  </ul>
  107.  *
  108.  *  <br><br>
  109.  *  <ul>
  110.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  111.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer Library</a></li>
  112.  *      <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>
  113.  *      <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>
  114.  *  </ul>
  115.  * 
  116.  * @author Lakshmi Krishnamurthy
  117.  */

  119. public class FritzJohnMultipliers {
  120.     private double[] _adblEquality = null;
  121.     private double[] _adblInequality = null;
  122.     private double _dblObjectiveCoefficient = java.lang.Double.NaN;

  124.     /**
  125.      * Construct a Standard KarushKuhnTucker (KKT) Instance of the Fritz John Multipliers
  126.      * 
  127.      * @param adblEquality Array of the Equality Constraint Coefficients
  128.      * @param adblInequality Array of the Inequality Constraint Coefficients
  129.      * 
  130.      * @return The KKT Instance of Fritz John Multipliers
  131.      */

  133.     public static final FritzJohnMultipliers KarushKuhnTucker (
  134.         final double[] adblEquality,
  135.         final double[] adblInequality)
  136.     {
  137.         try {
  138.             return new FritzJohnMultipliers (1., adblEquality, adblInequality);
  139.         } catch (java.lang.Exception e) {
  140.             e.printStackTrace();
  141.         }

  143.         return null;
  144.     }

  146.     /**
  147.      * FritzJohnMultipliers Constructor
  148.      * 
  149.      * @param dblObjectiveCoefficient The Objective Function Coefficient
  150.      * @param adblEquality Array of the Equality Constraint Coefficients
  151.      * @param adblInequality Array of the Inequality Constraint Coefficients
  152.      * 
  153.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  154.      */

  156.     public FritzJohnMultipliers (
  157.         final double dblObjectiveCoefficient,
  158.         final double[] adblEquality,
  159.         final double[] adblInequality)
  160.         throws java.lang.Exception
  161.     {
  162.         if (!org.drip.numerical.common.NumberUtil.IsValid (_dblObjectiveCoefficient = dblObjectiveCoefficient))
  163.             throw new java.lang.Exception ("FritzJohnMultipliers Constructor => Invalid Inputs");

  165.         _adblEquality = adblEquality;
  166.         _adblInequality = adblInequality;
  167.     }

  169.     /**
  170.      * Retrieve the Fritz John Objective Function Multiplier
  171.      * 
  172.      * @return The Fritz John Objective Function Multiplier
  173.      */

  175.     public double objectiveCoefficient()
  176.     {
  177.         return _dblObjectiveCoefficient;
  178.     }

  180.     /**
  181.      * Retrieve the Array of the Equality Constraint Coefficients
  182.      * 
  183.      * @return The Array of the Equality Constraint Coefficients
  184.      */

  186.     public double[] equalityConstraintCoefficient()
  187.     {
  188.         return _adblEquality;
  189.     }

  191.     /**
  192.      * Retrieve the Array of the Inequality Constraint Coefficients
  193.      * 
  194.      * @return The Array of the Inequality Constraint Coefficients
  195.      */

  197.     public double[] inequalityConstraintCoefficient()
  198.     {
  199.         return _adblInequality;
  200.     }

  202.     /**
  203.      * Retrieve the Number of Equality Multiplier Coefficients
  204.      * 
  205.      * @return The Number of Equality Multiplier Coefficients
  206.      */

  208.     public int numEqualityCoefficients()
  209.     {
  210.         return null == _adblEquality ? 0 : _adblEquality.length;
  211.     }

  213.     /**
  214.      * Retrieve the Number of Inequality Multiplier Coefficients
  215.      * 
  216.      * @return The Number of Inequality Multiplier Coefficients
  217.      */

  219.     public int numInequalityCoefficients()
  220.     {
  221.         return null == _adblInequality ? 0 : _adblInequality.length;
  222.     }

  224.     /**
  225.      * Retrieve the Number of Total KKT Multiplier Coefficients
  226.      * 
  227.      * @return The Number of Total KKT Multiplier Coefficients
  228.      */

  230.     public int numTotalCoefficients()
  231.     {
  232.         return numEqualityCoefficients() + numInequalityCoefficients();
  233.     }

  235.     /**
  236.      * Indicate of the Multipliers constitute Valid Dual Feasibility
  237.      * 
  238.      * @return TRUE - The Multipliers constitute Valid Dual Feasibility
  239.      */

  241.     public boolean dualFeasibilityCheck()
  242.     {
  243.         int iNumInequalityCoefficient = numInequalityCoefficients();

  245.         for (int i = 0; i < iNumInequalityCoefficient; ++i) {
  246.             if (0. > _adblInequality[i]) return false;
  247.         }

  249.         return true;
  250.     }
  251. }
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