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 "Optimization Solution" Golden Search Optimization Method
 Minimum = x = 0.999995177562161
 Value = f(x) = -10.899743449

 f(x) = 6.7 x4 - 3x3 + 5.2x2- 4x [ Interval Low: ] [ Interval High: ] [ Tolerance: 1.0e-5]

IMPLEMENTATION
Golden Search Method Optimization

The algorithm of the Golden Search method is similar to the algorithm of the Bisection Method (see Bisection Method algorithm). The Golden Search method uses an interval reduction factor that is based on the Fibonacci numbers, instead of just selecting the middle point of the interval for a given interval [xa,xn] that contains the minimum value for the function f(x), and the tolerance level as well.

Testing the Golden Search Method

We use the golden search method to find the minimum of a nonlinear function. To test it out as defined above, a new TestBisection() static method has been added and executed. Supporting code and methods are not shown.

static void TestGoldenSearch();
{
ListBox1.Items.Clear();
ListBox2.Items.Clear();
double result = Optimization.GoldenSearch(f, t1, t2, 1.0e-5);
ListBox1.Items.Add("x = " + result.ToString());
ListBox2.Items.Add("f(x) = " + f(result).ToString());
}

In order to test the golden sewarch method a nonlinear function f(x) = 6.7 x4 - 3x3 + 5.2x2- 4x was created. We can now test the minimum and function values based on different intervals. The user can manipulate interval values as desired

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