BarrierFixedPointFinder.java

package org.drip.function.rdtor1solver;

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

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 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>BarrierFixedPointFinder</i> invokes the Iterative Finders for locating the Fixed Point of
 * R<sup>d</sup> To R<sup>1</sup> Convex/Non-Convex Functions Under Inequality Constraints using Barrier
 * Sequences of decaying Strengths.
 *
 *	<br><br>
 *  <ul>
 *		<li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
 *		<li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
 *		<li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/feed/README.md">Function</a></li>
 *		<li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/feed/rdtor1solver/README.md">R<sup>d</sup> To R<sup>1</sup> Solver</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class BarrierFixedPointFinder
{
	private org.drip.function.definition.RdToR1 _objectiveFunction = null;
	private org.drip.function.rdtor1descent.LineStepEvolutionControl _lineStepEvolutionControl = null;
	private org.drip.function.definition.RdToR1[] _inequalityConstraintMultivariateFunctionArray = null;
	private org.drip.function.rdtor1solver.InteriorPointBarrierControl _interiorPointBarrierControl = null;

	/**
	 * BarrierFixedPointFinder Constructor
	 * 
	 * @param objectiveFunction The Objective Function
	 * @param inequalityConstraintMultivariateFunctionArray Array of Multivariate Inequality Constraint
	 * 		Functions
	 * @param interiorPointBarrierControl Interior Point Barrier Strength Control Parameters
	 * @param lineStepEvolutionControl Line Step Evolution Verifier Control Parameters
	 * 
	 * @throws java.lang.Exception Thrown if the Inputs are Invalid
	 */

	public BarrierFixedPointFinder (
		final org.drip.function.definition.RdToR1 objectiveFunction,
		final org.drip.function.definition.RdToR1[] inequalityConstraintMultivariateFunctionArray,
		final org.drip.function.rdtor1solver.InteriorPointBarrierControl interiorPointBarrierControl,
		final org.drip.function.rdtor1descent.LineStepEvolutionControl lineStepEvolutionControl)
		throws java.lang.Exception
	{
		if (null == (_objectiveFunction = objectiveFunction) ||
			null == (_inequalityConstraintMultivariateFunctionArray = inequalityConstraintMultivariateFunctionArray) ||
			null == (_interiorPointBarrierControl = interiorPointBarrierControl))
		{
			throw new java.lang.Exception ("BarrierFixedPointFinder Constructor => Invalid Inputs");
		}

		_lineStepEvolutionControl = lineStepEvolutionControl;
		int constraintCount = _inequalityConstraintMultivariateFunctionArray.length;

		if (0 == constraintCount)
		{
			throw new java.lang.Exception ("BarrierFixedPointFinder Constructor => Invalid Inputs");
		}

		for (int constraintIndex = 0;
			constraintIndex < constraintCount;
			++constraintIndex)
		{
			if (null == _inequalityConstraintMultivariateFunctionArray[constraintIndex])
			{
				throw new java.lang.Exception ("BarrierFixedPointFinder Constructor => Invalid Inputs");
			}
		}
	}

	/**
	 * Retrieve the Objective Function
	 * 
	 * @return The Objective Function
	 */

	public org.drip.function.definition.RdToR1 objectiveFunction()
	{
		return _objectiveFunction;
	}

	/**
	 * Retrieve the Array of Inequality Constraints
	 * 
	 * @return The Array of Inequality Constraints
	 */

	public org.drip.function.definition.RdToR1[] inequalityConstraintMultivariateFunctionArray()
	{
		return _inequalityConstraintMultivariateFunctionArray;
	}

	/**
	 * Retrieve the Line Step Evolution Interior Control Parameters
	 * 
	 * @return The Line Step Evolution Strength Control Parameters
	 */

	public org.drip.function.rdtor1descent.LineStepEvolutionControl lineStepEvolutionControl()
	{
		return _lineStepEvolutionControl;
	}

	/**
	 * Retrieve the Interior Point Barrier Control Parameters
	 * 
	 * @return The Interior Point Barrier Control Parameters
	 */

	public org.drip.function.rdtor1solver.InteriorPointBarrierControl interiorPointBarrierControl()
	{
		return _interiorPointBarrierControl;
	}

	/**
	 * Solve for the Optimal Variate-Inequality Constraint Multiplier Tuple using the Barrier Iteration
	 *  Parameters provided by the IPBC Instance
	 *  
	 * @param startingVariateArray The Starting Variate Sequence
	 * 
	 * @return The Optimal Variate-Inequality Constraint Multiplier Tuple
	 */

	public org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier solve (
		final double[] startingVariateArray)
	{
		double barrierStrength = _interiorPointBarrierControl.initialStrength();

		int outstandingDecaySteps = _interiorPointBarrierControl.decayStepCount();

		double barrierDecayVelocity = _interiorPointBarrierControl.decayVelocity();

		org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier variateConstraint = null;
		int constraintCount = _inequalityConstraintMultivariateFunctionArray.length;
		double[] startingConstraintMultiplierArray = new double[constraintCount];

		try
		{
			for (int constraintIndex = 0;
				constraintIndex < constraintCount;
				++constraintIndex)
			{
				startingConstraintMultiplierArray[constraintIndex] = barrierStrength /
					_inequalityConstraintMultivariateFunctionArray[constraintIndex].evaluate (
						startingVariateArray
					);
			}

			variateConstraint = new org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier (
				false,
				startingVariateArray,
				startingConstraintMultiplierArray
			);
		}
		catch (java.lang.Exception e)
		{
			e.printStackTrace();

			return null;
		}

		while (--outstandingDecaySteps >= 0)
		{
			try
			{
				org.drip.function.rdtor1solver.InteriorFixedPointFinder interiorFixedPointFinder =
					new org.drip.function.rdtor1solver.InteriorFixedPointFinder (
						_objectiveFunction,
						_inequalityConstraintMultivariateFunctionArray,
						_lineStepEvolutionControl,
						_interiorPointBarrierControl,
						barrierStrength
					);

				if (null == (
					variateConstraint = interiorFixedPointFinder.find (
						variateConstraint
					))
				)
				{
					return null;
				}
			}
			catch (java.lang.Exception e)
			{
				e.printStackTrace();

				return null;
			}

			barrierStrength *= barrierDecayVelocity;
		}

		return variateConstraint;
	}
}