// <copyright file="FindMinimum.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2017 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using IStation.Numerics.LinearAlgebra;
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using IStation.Numerics.Optimization;
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namespace IStation.Numerics
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{
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public static class FindMinimum
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{
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/// <summary>
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/// Find value x that minimizes the scalar function f(x), constrained within bounds, using the Golden Section algorithm.
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/// For more options and diagnostics consider to use <see cref="GoldenSectionMinimizer"/> directly.
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/// </summary>
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public static double OfScalarFunctionConstrained(Func<double, double> function, double lowerBound, double upperBound, double tolerance=1e-5, int maxIterations=1000)
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{
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var objective = ObjectiveFunction.ScalarValue(function);
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var result = GoldenSectionMinimizer.Minimum(objective, lowerBound, upperBound, tolerance, maxIterations);
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return result.MinimizingPoint;
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}
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/// <summary>
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/// Find vector x that minimizes the function f(x) using the Nelder-Mead Simplex algorithm.
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/// For more options and diagnostics consider to use <see cref="NelderMeadSimplex"/> directly.
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/// </summary>
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public static double OfScalarFunction(Func<double, double> function, double initialGuess, double tolerance = 1e-8, int maxIterations = 1000)
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{
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var objective = ObjectiveFunction.Value(v => function(v[0]));
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var result = NelderMeadSimplex.Minimum(objective, CreateVector.Dense(new[] { initialGuess }), tolerance, maxIterations);
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return result.MinimizingPoint[0];
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}
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/// <summary>
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/// Find vector x that minimizes the function f(x) using the Nelder-Mead Simplex algorithm.
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/// For more options and diagnostics consider to use <see cref="NelderMeadSimplex"/> directly.
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/// </summary>
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public static Tuple<double, double> OfFunction(Func<double, double, double> function, double initialGuess0, double initialGuess1, double tolerance = 1e-8, int maxIterations = 1000)
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{
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var objective = ObjectiveFunction.Value(v => function(v[0], v[1]));
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var result = NelderMeadSimplex.Minimum(objective, CreateVector.Dense(new[] { initialGuess0, initialGuess1 }), tolerance, maxIterations);
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return Tuple.Create(result.MinimizingPoint[0], result.MinimizingPoint[1]);
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}
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/// <summary>
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/// Find vector x that minimizes the function f(x) using the Nelder-Mead Simplex algorithm.
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/// For more options and diagnostics consider to use <see cref="NelderMeadSimplex"/> directly.
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/// </summary>
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public static Tuple<double, double, double> OfFunction(Func<double, double, double, double> function, double initialGuess0, double initialGuess1, double initialGuess2, double tolerance = 1e-8, int maxIterations = 1000)
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{
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var objective = ObjectiveFunction.Value(v => function(v[0], v[1], v[2]));
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var result = NelderMeadSimplex.Minimum(objective, CreateVector.Dense(new[] { initialGuess0, initialGuess1, initialGuess2 }), tolerance, maxIterations);
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return Tuple.Create(result.MinimizingPoint[0], result.MinimizingPoint[1], result.MinimizingPoint[2]);
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}
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/// <summary>
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/// Find vector x that minimizes the function f(x) using the Nelder-Mead Simplex algorithm.
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/// For more options and diagnostics consider to use <see cref="NelderMeadSimplex"/> directly.
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/// </summary>
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public static Vector<double> OfFunction(Func<Vector<double>, double> function, Vector<double> initialGuess, double tolerance=1e-8, int maxIterations=1000)
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{
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var objective = ObjectiveFunction.Value(function);
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var result = NelderMeadSimplex.Minimum(objective, initialGuess, tolerance, maxIterations);
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return result.MinimizingPoint;
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}
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/// <summary>
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/// Find vector x that minimizes the function f(x), constrained within bounds, using the Broyden–Fletcher–Goldfarb–Shanno Bounded (BFGS-B) algorithm.
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/// The missing gradient is evaluated numerically (forward difference).
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/// For more options and diagnostics consider to use <see cref="BfgsBMinimizer"/> directly.
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/// </summary>
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public static Vector<double> OfFunctionConstrained(Func<Vector<double>, double> function, Vector<double> lowerBound, Vector<double> upperBound, Vector<double> initialGuess, double gradientTolerance=1e-5, double parameterTolerance=1e-5, double functionProgressTolerance=1e-5, int maxIterations=1000)
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{
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var objective = ObjectiveFunction.Value(function);
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var objectiveWithGradient = new Optimization.ObjectiveFunctions.ForwardDifferenceGradientObjectiveFunction(objective, lowerBound, upperBound);
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var algorithm = new BfgsBMinimizer(gradientTolerance, parameterTolerance, functionProgressTolerance, maxIterations);
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var result = algorithm.FindMinimum(objectiveWithGradient, lowerBound, upperBound, initialGuess);
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return result.MinimizingPoint;
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}
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/// <summary>
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/// Find vector x that minimizes the function f(x) using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm.
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/// For more options and diagnostics consider to use <see cref="BfgsMinimizer"/> directly.
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/// An alternative routine using conjugate gradients (CG) is available in <see cref="ConjugateGradientMinimizer"/>.
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/// </summary>
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public static Vector<double> OfFunctionGradient(Func<Vector<double>, double> function, Func<Vector<double>, Vector<double>> gradient, Vector<double> initialGuess, double gradientTolerance=1e-5, double parameterTolerance=1e-5, double functionProgressTolerance=1e-5, int maxIterations=1000)
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{
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var objective = ObjectiveFunction.Gradient(function, gradient);
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var algorithm = new BfgsMinimizer(gradientTolerance, parameterTolerance, functionProgressTolerance, maxIterations);
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var result = algorithm.FindMinimum(objective, initialGuess);
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return result.MinimizingPoint;
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}
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/// <summary>
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/// Find vector x that minimizes the function f(x) using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm.
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/// For more options and diagnostics consider to use <see cref="BfgsMinimizer"/> directly.
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/// An alternative routine using conjugate gradients (CG) is available in <see cref="ConjugateGradientMinimizer"/>.
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/// </summary>
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public static Vector<double> OfFunctionGradient(Func<Vector<double>, Tuple<double, Vector<double>>> functionGradient, Vector<double> initialGuess, double gradientTolerance=1e-5, double parameterTolerance=1e-5, double functionProgressTolerance=1e-5, int maxIterations=1000)
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{
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var objective = ObjectiveFunction.Gradient(functionGradient);
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var algorithm = new BfgsMinimizer(gradientTolerance, parameterTolerance, functionProgressTolerance, maxIterations);
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var result = algorithm.FindMinimum(objective, initialGuess);
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return result.MinimizingPoint;
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}
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/// <summary>
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/// Find vector x that minimizes the function f(x), constrained within bounds, using the Broyden–Fletcher–Goldfarb–Shanno Bounded (BFGS-B) algorithm.
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/// For more options and diagnostics consider to use <see cref="BfgsBMinimizer"/> directly.
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/// </summary>
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public static Vector<double> OfFunctionGradientConstrained(Func<Vector<double>, double> function, Func<Vector<double>, Vector<double>> gradient, Vector<double> lowerBound, Vector<double> upperBound, Vector<double> initialGuess, double gradientTolerance=1e-5, double parameterTolerance=1e-5, double functionProgressTolerance=1e-5, int maxIterations=1000)
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{
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var objective = ObjectiveFunction.Gradient(function, gradient);
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var algorithm = new BfgsBMinimizer(gradientTolerance, parameterTolerance, functionProgressTolerance, maxIterations);
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var result = algorithm.FindMinimum(objective, lowerBound, upperBound, initialGuess);
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return result.MinimizingPoint;
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}
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/// <summary>
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/// Find vector x that minimizes the function f(x), constrained within bounds, using the Broyden–Fletcher–Goldfarb–Shanno Bounded (BFGS-B) algorithm.
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/// For more options and diagnostics consider to use <see cref="BfgsBMinimizer"/> directly.
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/// </summary>
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public static Vector<double> OfFunctionGradientConstrained(Func<Vector<double>, Tuple<double, Vector<double>>> functionGradient, Vector<double> lowerBound, Vector<double> upperBound, Vector<double> initialGuess, double gradientTolerance=1e-5, double parameterTolerance=1e-5, double functionProgressTolerance=1e-5, int maxIterations=1000)
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{
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var objective = ObjectiveFunction.Gradient(functionGradient);
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var algorithm = new BfgsBMinimizer(gradientTolerance, parameterTolerance, functionProgressTolerance, maxIterations);
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var result = algorithm.FindMinimum(objective, lowerBound, upperBound, initialGuess);
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return result.MinimizingPoint;
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}
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/// <summary>
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/// Find vector x that minimizes the function f(x) using the Newton algorithm.
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/// For more options and diagnostics consider to use <see cref="NewtonMinimizer"/> directly.
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/// </summary>
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public static Vector<double> OfFunctionGradientHessian(Func<Vector<double>, double> function, Func<Vector<double>, Vector<double>> gradient, Func<Vector<double>, Matrix<double>> hessian, Vector<double> initialGuess, double gradientTolerance=1e-8, int maxIterations=1000)
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{
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var objective = ObjectiveFunction.GradientHessian(function, gradient, hessian);
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var result = NewtonMinimizer.Minimum(objective, initialGuess, gradientTolerance, maxIterations);
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return result.MinimizingPoint;
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}
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/// <summary>
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/// Find vector x that minimizes the function f(x) using the Newton algorithm.
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/// For more options and diagnostics consider to use <see cref="NewtonMinimizer"/> directly.
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/// </summary>
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public static Vector<double> OfFunctionGradientHessian(Func<Vector<double>, Tuple<double, Vector<double>, Matrix<double>>> functionGradientHessian, Vector<double> initialGuess, double gradientTolerance=1e-8, int maxIterations=1000)
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{
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var objective = ObjectiveFunction.GradientHessian(functionGradientHessian);
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var result = NewtonMinimizer.Minimum(objective, initialGuess, gradientTolerance, maxIterations);
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return result.MinimizingPoint;
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}
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}
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}
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