TwoVariateConstrainedVariance.java

package org.drip.sample.semidefinite;

import org.drip.function.definition.RdToR1;
import org.drip.function.rdtor1.*;
import org.drip.function.rdtor1descent.LineStepEvolutionControl;
import org.drip.function.rdtor1solver.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;

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

/*!
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * 
 *  This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
 *      libraries targeting analysts and developers
 *      https://lakshmidrip.github.io/DRIP/
 *  
 *  DRIP is composed of four main libraries:
 *  
 *  - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
 *  - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
 *  - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
 *  - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
 * 
 *  - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
 *      Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
 *      Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
 *      Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
 *      Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
 * 
 *  - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
 *      Incorporator, Holdings Constraint, and Transaction Costs.
 * 
 *  - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
 * 
 *  - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
 * 
 *  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.
 */

/**
 * TwoVariateConstrainedVariance demonstrates the Application of the Interior Point Method for minimizing
 *  the Variance Across Two Variates under the Normalization Constraint.
 *
 * @author Lakshmi Krishnamurthy
 */

public class TwoVariateConstrainedVariance
{

    public static final void main (
        final String[] argumentArray)
        throws Exception
    {
        EnvManager.InitEnv (
            ""
        );

        double[][] covarianceMatrix = new double[][]
        {
            {0.09, 0.12},
            {0.12, 0.04}
        };

        double[] equalityConstraintRHSArray = new double[]
        {
            1.,
            1.
        };

        double equalityConstraintConstant = -1.;
        int objectiveDimension = covarianceMatrix.length;

        RdToR1[] equalityConstraintMultivariateFunctionArray = new AffineMultivariate[]
        {
            new AffineMultivariate (
                equalityConstraintRHSArray,
                equalityConstraintConstant
            )
        };

        int equalityConstraintCount = equalityConstraintMultivariateFunctionArray.length;

        AffineBoundMultivariate affineBoundMultivariateFunction1 = new AffineBoundMultivariate (
            true,
            0,
            2 + equalityConstraintCount,
            0.65
        );

        AffineBoundMultivariate affineBoundMultivariateFunction2 = new AffineBoundMultivariate (
            true,
            1,
            2 + equalityConstraintCount,
            0.65
        );

        AffineBoundMultivariate affineBoundMultivariateFunction3 = new AffineBoundMultivariate (
            false,
            0,
            2 + equalityConstraintCount,
            0.15
        );

        AffineBoundMultivariate affineBoundMultivariateFunction4 = new AffineBoundMultivariate (
            false,
            1,
            2 + equalityConstraintCount,
            0.15
        );

        RdToR1[] inequalityConstraintFunctionArray = new RdToR1[]
        {
            affineBoundMultivariateFunction1,
            affineBoundMultivariateFunction2,
            affineBoundMultivariateFunction3,
            affineBoundMultivariateFunction4
        };

        double barrierStrength = 1.;

        LagrangianMultivariate lagrangianMultivariate = new LagrangianMultivariate (
            new CovarianceEllipsoidMultivariate (
                covarianceMatrix
            ),
            equalityConstraintMultivariateFunctionArray
        );

        double[] startingVariateArray = ObjectiveConstraintVariateSet.Uniform (
            objectiveDimension,
            1
        );

        VariateInequalityConstraintMultiplier variateInequalityConstraintMultiplier =
            new BarrierFixedPointFinder (
                lagrangianMultivariate,
                inequalityConstraintFunctionArray,
                InteriorPointBarrierControl.Standard(),
                LineStepEvolutionControl.NocedalWrightStrongWolfe (
                    false
                )
            ).solve (
                startingVariateArray
            );

        System.out.println ("\n\n\t|----------------------------------------------------||");

        System.out.println (
            "\t| OPTIMAL VARIATES => " + FormatUtil.FormatDouble (variateInequalityConstraintMultiplier.variateArray()[0], 1, 5, 1.) +
            " | " + FormatUtil.FormatDouble (variateInequalityConstraintMultiplier.variateArray()[1], 1, 5, 1.) +
            " | " + FormatUtil.FormatDouble (lagrangianMultivariate.evaluate (variateInequalityConstraintMultiplier.variateArray()), 1, 5, 1.) + " ||"
        );

        System.out.println ("\t|----------------------------------------------------||\n\n");

        int stepDown = 20;

        double[] constraintMultiplierArray = new double[inequalityConstraintFunctionArray.length];

        for (int inequalityConstraintFunctionIndex = 0;
            inequalityConstraintFunctionIndex < inequalityConstraintFunctionArray.length;
            ++inequalityConstraintFunctionIndex)
        {
            constraintMultiplierArray[inequalityConstraintFunctionIndex] = barrierStrength /
                inequalityConstraintFunctionArray[inequalityConstraintFunctionIndex].evaluate (
                    startingVariateArray
                );
        }

        variateInequalityConstraintMultiplier = new VariateInequalityConstraintMultiplier (
            false,
            startingVariateArray,
            constraintMultiplierArray
        );

        ConvergenceControl convergenceControl = new ConvergenceControl (
            ConvergenceControl.OBJECTIVE_FUNCTION_SEQUENCE_CONVERGENCE,
            5.0e-02,
            1.0e-06,
            70
        );

        System.out.println ("\t|-------------------------------------------------||");

        System.out.println ("\t|    BARRIER    =>      VARIATES       | VARIANCE ||");

        System.out.println ("\t|-------------------------------------------------||");

        while (--stepDown > 0)
        {
            variateInequalityConstraintMultiplier = new InteriorFixedPointFinder (
                lagrangianMultivariate,
                inequalityConstraintFunctionArray,
                LineStepEvolutionControl.NocedalWrightStrongWolfe (
                    false
                ),
                convergenceControl,
                barrierStrength
            ).find (
                variateInequalityConstraintMultiplier
            );

            startingVariateArray = variateInequalityConstraintMultiplier.variateArray();

            System.out.println (
                "\t| " + FormatUtil.FormatDouble (barrierStrength, 1, 10, 1.) +
                " => " + FormatUtil.FormatDouble (
                    variateInequalityConstraintMultiplier.variateArray()[0], 1, 5, 1.
                ) +
                " | " + FormatUtil.FormatDouble (
                    variateInequalityConstraintMultiplier.variateArray()[1], 1, 5, 1.
                ) +
                " | " + FormatUtil.FormatDouble (
                    lagrangianMultivariate.evaluate (
                        variateInequalityConstraintMultiplier.variateArray()
                    ), 1, 5, 1.
                ) + " ||"
            );

            barrierStrength *= 0.5;
        }

        System.out.println ("\t|-------------------------------------------------||\n\n");
    }
}