StrengthenedChvatalGomoryCut.java

package org.drip.linearprogram.cuttingplane;

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

/*!
 * Copyright (C) 2020 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>StrengthenedChvatalGomoryCut</i> implements the Strengthened Chvatal Gomory Cut. The References are:
 * 
 * <br><br>
 *  <ul>
 *      <li>
 *          Burdet, C. A., and E. L. Johnson (1977): A Sub-additive Approach to Solve Linear Integer Programs
 *              <i>Annals of Discrete Mathematics</i> <b>1</b> 117-143
 *      </li>
 *      <li>
 *          Chvatal, V. (1973): Edmonds Polytopes in a Hierarchy of Combinatorial Problems <i>Discrete
 *              Mathematics</i> <b>4 (4)</b> 305-337
 *      </li>
 *      <li>
 *          Gomory, R. E. (1958): Outline of an Algorithm for Integer Solutions to Linear Programs
 *              <i>Bulletin of the American Mathematical Society</i> <b>64 (5)</b> 275-278
 *      </li>
 *      <li>
 *          Kelley, J. E. (1960): The Cutting Plane Method for Solving Convex Problems <i>Journal for the
 *              Society of the Industrial and Applied Mathematics</i> <b>8 (4)</b> 703-712
 *      </li>
 *      <li>
 *          Letchford, A. N. and A. Lodi (2002): Strengthening Chvatal-Gomory Cuts and Gomory Fractional Cuts
 *              <i>Operations Research Letters</i> <b>30 (2)</b> 74-82
 *      </li>
 *  </ul>
 *
 *  <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AssetAllocationAnalyticsLibrary.md">Asset Allocation Analytics</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/linearprogram/README.md">Linear Programming Solution Suite</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/linearprogram/cuttingplane/README.md">Polyhedral Cutting Plane Generation Schemes</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class StrengthenedChvatalGomoryCut
    extends org.drip.linearprogram.cuttingplane.ChvatalGomoryCut
{
    private int _t = -1;

    /**
     * StrengthenedChvatalGomoryCut Constructor
     * 
     * @param aGrid "A" Constraint Grid
     * @param bArray "b" Constraint Array
     * @param lambdaArray The Lambda Array
     * @param t Strengthening Integer
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public StrengthenedChvatalGomoryCut (
        final int[][] aGrid,
        final int[] bArray,
        final double[] lambdaArray,
        final int t)
        throws java.lang.Exception
    {
        super (
            aGrid,
            bArray,
            lambdaArray
        );

        if (0 >= (_t = t))
        {
            throw new java.lang.Exception (
                "StrengthenedChvatalGomoryCut Constructor => Invalid Inputs"
            );
        }
    }

    /**
     * Retrieve the Strengthening Integer
     * 
     * @return The Strengthening Integer
     */

    public int t()
    {
        return _t;
    }

    /**
     * Verify if the Variate Array satisfies the Constraint
     * 
     * @param variateArray The Input Variate Array
     * 
     * @return TRUE - The Variate Array satisfies the Constraint
     */

    public boolean verify (
        final int[] variateArray)
        throws java.lang.Exception
    {
        if (!super.verify (
            variateArray
        ))
        {
            return false;
        }

        int[] bArray = bArray();

        int[][] aGrid = aGrid();

        double[] lambdaArray = lambdaArray();

        double lhs = 0;
        double rhs = 0.;
        int dimension = aGrid.length;
        int constraintCount = bArray.length;

        for (int constraintIndex = 0;
            constraintIndex < constraintCount;
            ++constraintIndex)
        {
            double lambdaTFraction = org.drip.numerical.common.NumberUtil.Fractional (
                lambdaArray[constraintIndex] * _t
            );

            for (int dimensionIndex = 0;
                dimensionIndex < dimension;
                ++dimensionIndex)
            {
                lhs += variateArray[dimensionIndex] * lambdaTFraction *
                    aGrid[constraintIndex][dimensionIndex];
            }

            rhs  = rhs + lambdaTFraction * bArray[constraintIndex];
        }

        return (int) lhs <= (int) rhs;
    }
}