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"Optimization Solution"
Golden Search Optimization Method
Minimum =
      Value =

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



Other Implementations...


Graphics and Animation
Sample Applications
Ore Extraction Optimization
Vectors and Matrices
Complex Numbers and Functions
Ordinary Differential Equations - Euler Method
Ordinary Differential Equations 2nd-Order Runge-Kutta
Ordinary Differential Equations 4th-Order Runge-Kutta
Higher Order Differential Equations
Nonlinear Systems
Numerical Integration
Numerical Differentiation
Function Evaluation

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