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 "Optimization Solution" Differential Evolution Optimization Method
 MIN: Iterations + BestValue 50, f(x) = -6.49037321131064 100, f(x) = -6.43592237938073 150, f(x) = -6.5280061278972 200, f(x) = -6.33589151634384 MINIMUM: -6.54589200746287 New Iteration = 0, f(x) = -5.45808852659871 BestMember x = (0.151779787685619, -1.63988523787125) x = (0.301366995877292, -1.55199894801532) x = (0.272569255098966, -1.62043138809829) x = (0.374783036473572, -1.64170127773737) AT: (0.374783036473572, -1.64170127773737) x = (-0.104594416033753, -1.77965316724947)

 MAX: 50, f(x) = -8.07881201738038 100, f(x) = -8.09206137880087 150, f(x) = -7.47250957282821 200, f(x) = -8.10682998803228 MAXIMUM: 3.94548306853789 New Iteration = 0, f(x) = -7.30653393225846 x = (0.0274199796968233, 1.54107735207395) x = (-0.0540832197545484, 1.60329351992939) x = (0.269247078089624, 1.64013824698201) x = (0.00696259660001908, 1.60172316254188) AT: (0.00696259660001908, 1.60172316254188) x = (0.233743787851997, 1.43375794749416)

 Enter new iteration: Iteration =

IMPLEMENTATION
Differential Evolution Method Optimization

This method may be considered as a random-search technique. Stochastic methods are efficient techniques for finding the global minimum of a function with multiple variables. In general, thse type of optimization techniques are inspired by biological processes and are called evolutionary algorithms.

Several advantages of using evolutionary algorithms over the traditional optimization methods include:

• Optimize with continous or discrete variables.
• Usually do not require derivative information.
• Deal with a large number of variables.
• Work with numerically generated data, experimental data, or analytical functions.

Algorithm Creation

Using the "peaks" function, which is used extensively in Matlab:

 f(x,y) = 3(1-x)2 e-x2 - (y + 1)2 - 10( 1/5x - x3 - y5) e-x2

This function has several local minima and maxima. It is also possible to find the global maximum for the peaks function by simply returning the negative value of the function.

Testing the Differential Evolution Method

To test it out we find the the minimum and maximum points of the peaks function. We ran the program using different iteration parameters(4). The user can manipulate and test it further by manually entering new iterations.

Supporting code and methods are not shown.

 Other Implementations...

 Object-Oriented Implementation 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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EIGENVALUE
SOLUTIONS...

> Rayleigh-Quotient Method

> Cubic Spline Method

 Applied Mathematical Algorithms
 ComplexFunctions NonLinear Differentiation Integration
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