# Optimization In One Dimension in C# QuickStart Sample

Illustrates the use of the Brent and Golden Section optimizer classes in the Extreme.Mathematics.Optimization namespace for one-dimensional optimization in C#.

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``````using System;
// The optimization classes resides in the
// Extreme.Mathematics.EquationSolvers namespace.
using Extreme.Mathematics.Optimization;
// Function delegates reside in the Extreme.Mathematics
// namespace.
using Extreme.Mathematics;

namespace Extreme.Numerics.QuickStart.CSharp
{
/// <summary>
/// Illustrates the use of the Brent and Golden Section optimizers
/// in the Extreme.Mathematics.Optimization namespace of Extreme Numerics.NET.
/// </summary>
class OptimizationIn1D
{
static void Main(string[] args)
{
// The license is verified at runtime. We're using
// https://numerics.net/trial-key
// Several algorithms exist for optimizing functions
// in one variable. The most common one is
// Brent's algorithm.

// The function we are trying to minimize is called the
// objective function and must be provided as a Func<double, double>.
// FunctionDelegates QuickStart sample.
Func<double, double> f1 = new Func<double, double>(TestFunction1);
Func<double, double> f2 = new Func<double, double>(TestFunction2);

//
// Brent's algorithm
//

// Now let's create the BrentOptimizer object.
BrentOptimizer optimizer = new BrentOptimizer();

// Set the objective function:
optimizer.ObjectiveFunction = f1;
if

// Optimizers can find either a minimum or a maximum.
// Which of the two is specified by the ExtremumType
// property
optimizer.ExtremumType = ExtremumType.Minimum;

// The first phase is to find an interval that contains
// a local minimum. This is done by the FindBracket method.
optimizer.FindBracket(0, 3);
// You can verify that an interval was found from the
// IsBracketValid property:
if (!optimizer.IsBracketValid)

// Finally, we can run the optimizer by calling the FindExtremum method:
optimizer.FindExtremum();

Console.WriteLine("Function 1: x^3 - 2x - 5");
// The Status property indicates
// the result of running the algorithm.
Console.WriteLine("  Status: {0}", optimizer.Status);
// The result is available through the
// Result property.
Console.WriteLine("  Minimum: {0}", optimizer.Result);
double exactResult = Math.Sqrt(2/3.0);
double result = optimizer.Extremum;
Console.WriteLine("  Exact minimum: {0}", exactResult);

// You can find out the estimated error of the result
// through the EstimatedError property:
Console.WriteLine("  Estimated error: {0}", optimizer.EstimatedError);
Console.WriteLine("  Actual error: {0}", Math.Abs(result - exactResult));
Console.WriteLine("  # iterations: {0}", optimizer.IterationsNeeded);

Console.WriteLine("Function 2: 1/Exp(x*x - 0.7*x +0.2)");
// You can also perform these calculations more directly
// using the FindMinimum or FindMaximum methods. This implicitly
// calls the FindBracket method.
result = optimizer.FindMaximum(f2, 0);
Console.WriteLine("  Maximum: {0}", result);
Console.WriteLine("  Actual maximum: {0}", 0.35);
Console.WriteLine("  Estimated error: {0}", optimizer.EstimatedError);
Console.WriteLine("  Actual error: {0}", result - 0.35);
Console.WriteLine("  # iterations: {0}", optimizer.IterationsNeeded);

//
// Golden section search
//

// A slower but simpler algorithm for finding an extremum
// is the golden section search. It is implemented by the
// GoldenSectionMinimizer class:
GoldenSectionOptimizer optimizer2 = new GoldenSectionOptimizer();

Console.WriteLine("Using Golden Section optimizer:");
result = optimizer2.FindMaximum(f2, 0);
Console.WriteLine("  Maximum: {0}", result);
Console.WriteLine("  Actual maximum: {0}", 0.35);
Console.WriteLine("  Estimated error: {0}", optimizer2.EstimatedError);
Console.WriteLine("  Actual error: {0}", result - 0.35);
Console.WriteLine("  # iterations: {0}", optimizer2.IterationsNeeded);

Console.Write("Press Enter key to exit...");
}

// Minimum at x = Sqrt(2/3) = 0.816496580927726
static double TestFunction1(double x)
{
return x*x*x - 2*x - 5;
}

// Maximum at x = 0.35
static double TestFunction2(double x)
{
return 1/Math.Exp(x*x - 0.7*x +0.2);
}
}
}``````