NecessarySufficientConditions.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>NecessarySufficientConditions</i> holds the Results of the Verification of the Necessary and the
  82.  * Sufficient Conditions at the specified (possibly) Optimal Variate and the corresponding Fritz John
  83.  * Multiplier Suite. The References are:
  84.  * 
  85.  * <br><br>
  86.  *  <ul>
  87.  *      <li>
  88.  *          Boyd, S., and L. van den Berghe (2009): <i>Convex Optimization</i> <b>Cambridge University
  89.  *              Press</b> Cambridge UK
  90.  *      </li>
  91.  *      <li>
  92.  *          Eustaquio, R., E. Karas, and A. Ribeiro (2008): <i>Constraint Qualification for Nonlinear
  93.  *              Programming</i> <b>Federal University of Parana</b>
  94.  *      </li>
  95.  *      <li>
  96.  *          Karush, A. (1939): <i>Minima of Functions of Several Variables with Inequalities as Side
  97.  *          Constraints</i> <b>University of Chicago</b> Chicago IL
  98.  *      </li>
  99.  *      <li>
  100.  *          Kuhn, H. W., and A. W. Tucker (1951): Nonlinear Programming <i>Proceedings of the Second Berkeley
  101.  *              Symposium</i> <b>University of California</b> Berkeley CA 481-492
  102.  *      </li>
  103.  *      <li>
  104.  *          Ruszczynski, A. (2006): <i>Nonlinear Optimization</i> <b>Princeton University Press</b> Princeton
  105.  *              NJ
  106.  *      </li>
  107.  *  </ul>
  108.  *
  109.  *  <br><br>
  110.  *  <ul>
  111.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  112.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer Library</a></li>
  113.  *      <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>
  114.  *      <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>
  115.  *  </ul>
  116.  * 
  117.  * @author Lakshmi Krishnamurthy
  118.  */

  120. public class NecessarySufficientConditions {
  121.     private double[] _adblVariate = null;
  122.     private boolean _bCheckForMinima = false;
  123.     private org.drip.optimization.constrained.FritzJohnMultipliers _fjm = null;
  124.     private org.drip.optimization.necessary.ConditionQualifierFONC _cqFONC = null;
  125.     private org.drip.optimization.necessary.ConditionQualifierSOSC _cqSOSC = null;
  126.     private org.drip.optimization.necessary.ConditionQualifierDualFeasibility _cqDualFeasibility = null;
  127.     private org.drip.optimization.necessary.ConditionQualifierPrimalFeasibility _cqPrimalFeasibility =
  128.         null;
  129.     private org.drip.optimization.necessary.ConditionQualifierComplementarySlackness
  130.         _cqComplementarySlackness = null;

  132.     /**
  133.      * Create a Standard Instance of NecessarySufficientConditions
  134.      * 
  135.      * @param adblVariate The Candidate Variate Array
  136.      * @param fjm The Fritz John Multipliers
  137.      * @param bCheckForMinima TRUE - Check For Minima
  138.      * @param bPrimalFeasibilityValidity The Primal Feasibility Validity
  139.      * @param bDualFeasibilityValidity The Dual Feasibility Validity
  140.      * @param bComplementarySlacknessValidity The Complementary Slackness Validity
  141.      * @param bFONCValidity The FONC Validity
  142.      * @param bSOSCValidity The SOSC Validity
  143.      * 
  144.      * @return The Standard NecessarySufficientConditions Instance
  145.      */

  147.     public static final NecessarySufficientConditions Standard (
  148.         final double[] adblVariate,
  149.         final org.drip.optimization.constrained.FritzJohnMultipliers fjm,
  150.         final boolean bCheckForMinima,
  151.         final boolean bPrimalFeasibilityValidity,
  152.         final boolean bDualFeasibilityValidity,
  153.         final boolean bComplementarySlacknessValidity,
  154.         final boolean bFONCValidity,
  155.         final boolean bSOSCValidity)
  156.     {
  157.         try {
  158.             return new NecessarySufficientConditions (adblVariate, fjm, bCheckForMinima, new
  159.                 org.drip.optimization.necessary.ConditionQualifierPrimalFeasibility
  160.                     (bPrimalFeasibilityValidity), new
  161.                         org.drip.optimization.necessary.ConditionQualifierDualFeasibility
  162.                             (bDualFeasibilityValidity), new
  163.                                 org.drip.optimization.necessary.ConditionQualifierComplementarySlackness
  164.                                     (bComplementarySlacknessValidity), new
  165.                                         org.drip.optimization.necessary.ConditionQualifierFONC
  166.                                             (bFONCValidity), new
  167.                                                 org.drip.optimization.necessary.ConditionQualifierSOSC
  168.                                                     (bSOSCValidity));
  169.         } catch (java.lang.Exception e) {
  170.             e.printStackTrace();
  171.         }

  173.         return null;
  174.     }

  176.     /**
  177.      * NecessarySufficientConditions Constructor
  178.      * 
  179.      * @param adblVariate The Candidate Variate Array
  180.      * @param fjm The Fritz John Multipliers
  181.      * @param bCheckForMinima TRUE - Check For Minima
  182.      * @param cqPrimalFeasibility The Primal Feasibility Necessary Condition
  183.      * @param cqDualFeasibility The Dual Feasibility Necessary Condition
  184.      * @param cqComplementarySlackness The Complementary Slackness Necessary Condition
  185.      * @param cqFONC The First Order Necessary Condition
  186.      * @param cqSOSC The Second Order Sufficiency Condition
  187.      * 
  188.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  189.      */

  191.     public NecessarySufficientConditions (
  192.         final double[] adblVariate,
  193.         final org.drip.optimization.constrained.FritzJohnMultipliers fjm,
  194.         final boolean bCheckForMinima,
  195.         final org.drip.optimization.necessary.ConditionQualifierPrimalFeasibility cqPrimalFeasibility,
  196.         final org.drip.optimization.necessary.ConditionQualifierDualFeasibility cqDualFeasibility,
  197.         final org.drip.optimization.necessary.ConditionQualifierComplementarySlackness
  198.             cqComplementarySlackness,
  199.         final org.drip.optimization.necessary.ConditionQualifierFONC cqFONC,
  200.         final org.drip.optimization.necessary.ConditionQualifierSOSC cqSOSC)
  201.         throws java.lang.Exception
  202.     {
  203.         if (null == (_adblVariate = adblVariate) || 0 == _adblVariate.length || null == (_fjm = fjm) || null
  204.             == (_cqPrimalFeasibility = cqPrimalFeasibility) || null == (_cqDualFeasibility =
  205.                 cqDualFeasibility) || null == (_cqComplementarySlackness = cqComplementarySlackness) || null
  206.                     == (_cqFONC = cqFONC) || null == (_cqSOSC = cqSOSC))
  207.             throw new java.lang.Exception ("NecessarySufficientConditions Constructor => Invalid Inputs");

  209.         _bCheckForMinima = bCheckForMinima;
  210.     }

  212.     /**
  213.      * Retrieve the Candidate Variate Array
  214.      * 
  215.      * @return The Candidate Variate Array
  216.      */

  218.     public double[] variate()
  219.     {
  220.         return _adblVariate;
  221.     }

  223.     /**
  224.      * Retrieve the Fritz John Mutipliers
  225.      * 
  226.      * @return The Fritz John Mutipliers
  227.      */

  229.     public org.drip.optimization.constrained.FritzJohnMultipliers fritzJohnMultipliers()
  230.     {
  231.         return _fjm;
  232.     }

  234.     /**
  235.      * Retrieve if the Check corresponds to Local Minima
  236.      * 
  237.      * @return TRUE - The Check corresponds to Local Minima
  238.      */

  240.     public boolean checkFroMinima()
  241.     {
  242.         return _bCheckForMinima;
  243.     }

  245.     /**
  246.      * Retrieve the Primal Feasibility Necessary Condition
  247.      * 
  248.      * @return The Primal Feasibility Necessary Condition
  249.      */

  251.     public org.drip.optimization.necessary.ConditionQualifierPrimalFeasibility primalFeasibility()
  252.     {
  253.         return _cqPrimalFeasibility;
  254.     }

  256.     /**
  257.      * Retrieve the Dual Feasibility Necessary Condition
  258.      * 
  259.      * @return The Dual Feasibility Necessary Condition
  260.      */

  262.     public org.drip.optimization.necessary.ConditionQualifierDualFeasibility dualFeasibility()
  263.     {
  264.         return _cqDualFeasibility;
  265.     }

  267.     /**
  268.      * Retrieve the Complementary Slackness Necessary Condition
  269.      * 
  270.      * @return The Complementary Slackness Necessary Condition
  271.      */

  273.     public org.drip.optimization.necessary.ConditionQualifierComplementarySlackness
  274.         complementarySlackness()
  275.     {
  276.         return _cqComplementarySlackness;
  277.     }

  279.     /**
  280.      * Retrieve the First Order Necessary Condition
  281.      * 
  282.      * @return The First Order Necessary Condition
  283.      */

  285.     public org.drip.optimization.necessary.ConditionQualifierFONC fonc()
  286.     {
  287.         return _cqFONC;
  288.     }

  290.     /**
  291.      * Retrieve the Second Order Sufficiency Condition
  292.      * 
  293.      * @return The Second Order Sufficiency Condition
  294.      */

  296.     public org.drip.optimization.necessary.ConditionQualifierSOSC sosc()
  297.     {
  298.         return _cqSOSC;
  299.     }

  301.     /**
  302.      * Indicate the Necessary/Sufficient Validity across all the Condition Qualifiers
  303.      * 
  304.      * @return TRUE - The Necessary/Sufficient Criteria is satisfied across all the Condition Qualifiers
  305.      */

  307.     public boolean valid()
  308.     {
  309.         return _cqPrimalFeasibility.valid() && _cqDualFeasibility.valid() &&
  310.             _cqComplementarySlackness.valid() && _cqFONC.valid() && _cqSOSC.valid();
  311.     }

  313.     /**
  314.      * Retrieve the Array of Condition Orders
  315.      * 
  316.      * @return The Array of Condition Orders
  317.      */

  319.     public java.lang.String[] conditionOrder()
  320.     {
  321.         return new java.lang.String[] {"ZERO ORDER: " + _cqPrimalFeasibility.display() + " >> " +
  322.             _cqDualFeasibility.display() + " >> " + _cqComplementarySlackness.display(), "FIRST ORDER: " +
  323.                 _cqFONC.display(), "SECOND ORDER: " + _cqSOSC.display()};
  324.     }
  325. }
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