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;
}
}