Optimization.Simplex Method (TRealFunction, double[], [In] double[], [In] object[], out double, out TOptStopReason, [In] TMtxFloatPrecision, int, double, [In] TStrings)

Minimizes the function of several variables by using the Nelder-Mead (Simplex) optimization method.

Syntax

Visual Basic

public static int Simplex(TRealFunction Func, ref double[] Pars, [In] double[] Consts, [In] object[] ObjConst, out double FMin, out TOptStopReason StopReason, [In] TMtxFloatPrecision FloatPrecision, int MaxIter, double Tolerance, [In] TStrings Verbose);

Parameters

Parameters	Description
TRealFunction Func	Real function (must be of TRealFunction type) to be minimized.
ref double[] Pars	Stores the initial estimates for parameters (minimum estimate). After the call to routine returns adjusted calculated values (minimum position).
[In] double[] Consts	Additional Fun constant parameteres (can be/is usually nil).
[In] object[] ObjConst	Additional Fun constant parameteres (can be/is usually nil).
out double FMin	Returns function value at minimum.
out TOptStopReason StopReason	Returns reason why minimum search stopped (see TOptStopReason).
[In] TMtxFloatPrecision FloatPrecision	Specifies the floating point precision to be used by the routine.
int MaxIter	Maximum allowed numer of minimum search iterations.
double Tolerance	Desired Pars - minimum position tolerance.
[In] TStrings Verbose	If assigned, stores Fun, evaluated at each iteration step. Optionally, you can also pass TOptControl object to the Verbose parameter. This allows the optimization procedure to be interrupted from another thread and optionally also allows logging and iteration count monitoring.

Returns

the number of iterations required to reach the solution(minimum) within given tolerance.

Remarks

Minimizes the function of several variables by using the Nelder-Mead (Simplex) optimization method. The advantage of Simplex method is it does not require gradient or Hessian.

See Also

TRealFunction

Example

Problem: Find the minimum of the "Banana" function by using the Nelder-Mead (Simplex) method.

Solution:The Banana function is defined by the following equation:

private double Banana(TVec x, TVec c, params object[] o) { return 100*Math387.IntPower(x[1] - Math387.IntPower(x[0],2),2) + Math387.IntPower(1 - x[0],2); } private void Example() { double[2] x; double fmin; TOptStopReason StopReason; // initial estimates for x1 and x2 x[0] = 0; x[1] = 0; int iters = Simplex(Banana,x,null,null,out fmin,out StopReason, TMtxFloatPrecision.mvDouble, 1000,1.0E-8,null); // stop if Iters >1000 or Tolerance < 1e-8 // Returns x = [1,1] and FMin = 0, meaning x1=1, x2=1 and minimum value is 0 }

Group

Simplex Method

Links

Optimization Class, Optimization Members, Dew.Math.Units Namespace, Simplex Method, Example, See Also

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