NSphereSurfaceExtremization.java

package org.drip.sample.optimizer;

import org.drip.function.definition.RdToR1;
import org.drip.function.rdtor1.LagrangianMultivariate;
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.
 */

/**
 * NSphereSurfaceExtremization computes the Equality-Constrained Extrema of the Specified Function along the
 *  Surface of an N-Sphere using Lagrange Multipliers.
 *
 * @author Lakshmi Krishnamurthy
 */

public class NSphereSurfaceExtremization
{

    private static final void Solve (
        final NewtonFixedPointFinder newtonFixedPointFinder,
        final double[] startingVariateArray)
        throws Exception
    {
        System.out.println ("\n\t|------------------------------------||");

        String strDump = "\t| STARTER: [";

        strDump += FormatUtil.FormatDouble (startingVariateArray[0], 1, 4, 1.) + ",";

        strDump += FormatUtil.FormatDouble (startingVariateArray[1], 1, 4, 1.) + ",";

        strDump += FormatUtil.FormatDouble (startingVariateArray[2], 1, 4, 1.);

        System.out.println (strDump + "] ||");

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

        double[] variateArray = newtonFixedPointFinder.convergeVariate (
            new VariateInequalityConstraintMultiplier (
                false,
                startingVariateArray,
                null
            )
        ).variateArray();

        System.out.println (
            "\t| Optimal X      : " + FormatUtil.FormatDouble (variateArray[0], 1, 4, 1.) + "           ||"
        );

        System.out.println (
            "\t| Optimal Y      : " + FormatUtil.FormatDouble (variateArray[1], 1, 4, 1.) + "           ||"
        );

        System.out.println (
            "\t| Optimal Lambda : " + FormatUtil.FormatDouble (variateArray[2], 1, 4, 1.) + "           ||"
        );

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

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

        RdToR1 variateSumObjectiveFunction = new RdToR1 (
            null
        )
        {
            @Override public double evaluate (
                final double[] variateArray)
                throws Exception
            {
                return variateArray[0] * variateArray[0] * variateArray[1];
            }

            @Override public int dimension()
            {
                return 2;
            }

            @Override public double[] jacobian (
                final double[] variateArray)
            {
                double[] jacobian = new double[2];
                jacobian[0] = 2. * variateArray[0] * variateArray[1];
                jacobian[1] = variateArray[0] * variateArray[0];
                return jacobian;
            }

            @Override public double[][] hessian (
                final double[] variateArray)
            {
                double[][] hessian = new double[2][2];
                hessian[0][0] = 2. * variateArray[1];
                hessian[0][1] = 2. * variateArray[0];
                hessian[1][0] = 2. * variateArray[0];
                hessian[1][1] = 0.;
                return hessian;
            }
        };

        RdToR1 sphereSurfaceConstraintFunction = new RdToR1 (
            null
        )
        {
            @Override public double evaluate (
                final double[] variateArray)
                throws Exception
            {
                return variateArray[0] * variateArray[0] + variateArray[1] * variateArray[1] - 3.;
            }

            @Override public int dimension()
            {
                return 2;
            }

            @Override public double[] jacobian (
                final double[] variateArray)
            {
                double[] jacobian = new double[2];
                jacobian[0] = 2. * variateArray[0];
                jacobian[1] = 2. * variateArray[1];
                return jacobian;
            }

            @Override public double[][] hessian (
                final double[] variateArray)
            {
                double[][] hessian = new double[2][2];
                hessian[0][0] = 2.;
                hessian[0][1] = 0.;
                hessian[1][0] = 0.;
                hessian[1][1] = 2.;
                return hessian;
            }
        };

        NewtonFixedPointFinder newtonFixedPointFinder = new NewtonFixedPointFinder (
            new LagrangianMultivariate (
                variateSumObjectiveFunction,
                new RdToR1[]
                {
                    sphereSurfaceConstraintFunction
                }
            ),
            LineStepEvolutionControl.NocedalWrightStrongWolfe (
                false
            ),
            ConvergenceControl.Standard()
        );

        Solve (
            newtonFixedPointFinder,
            new double[]
            {
                2.,
                1.,
                1.
            }
        );

        Solve (
            newtonFixedPointFinder,
            new double[]
            {
                -2.,
                 1.,
                 1.
            }
        );

        Solve (
            newtonFixedPointFinder,
            new double[] {
                 2.,
                -1.,
                 1.
            }
        );

        Solve (
            newtonFixedPointFinder,
            new double[]
            {
                -2.,
                -1.,
                 1.
            }
        );

        Solve (
            newtonFixedPointFinder,
            new double[]
            {
                0.,
                1.,
                0.
            }
        );

        Solve (
            newtonFixedPointFinder,
            new double[]
            {
                 0.,
                -1.,
                 0.
            }
        );
    }
}