Optimization.Simplex Function

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

Pascal

function Simplex(Func: TRealFunction; var Pars: Array of double; Const Consts: array of double; Const ObjConst: Array of TObject; out FMin: double; out StopReason: TOptStopReason; const FloatPrecision: TMtxFloatPrecision = mvDouble; MaxIter: Integer = 500; Tolerance: double = 1.0E-8; const Verbose: TStrings = nil): Integer; overload;

File

Optimization

Parameters

Parameters	Description
Func	Real function (must be of TRealFunction type) to be minimized.
Pars	Stores the initial estimates for parameters (minimum estimate). After the call to routine returns adjusted calculated values (minimum position).
Consts	Additional Fun constant parameteres (can be/is usually nil).
ObjConst	Additional Fun constant parameteres (can be/is usually nil).
FMin	Returns function value at minimum.
StopReason	Returns reason why minimum search stopped (see TOptStopReason).
FloatPrecision	Specifies the floating point precision to be used by the routine.
MaxIter	Maximum allowed numer of minimum search iterations.
Tolerance	Desired Pars - minimum position tolerance.
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.

Description

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:

Uses MtxVec, Math387, Optimization; function Banana(const Pars: TVec; const Consts: TVec; Const OConsts: Array of TObject): double; begin Banana := 100*Sqr(Pars[1]-Sqr(Pars[0]))+Sqr(1-Pars[0]); end; procedure Example; var Iters : integer; Pars : Array [0..1] of double; StopReason : TOptStopReason; begin // initial estimates for x1 and x2 Pars[0] := 0; Pars[1] := 0; Iters := Simplex(Banana,Pars,[],[],FMin,StopReason,mvDouble,1000); // stop if Iters >1000 or Tolerance < 1e-8 // Returns Pars = [1,1] and FMin = 0, meaning x1=1, x2=1 and minimum value is 0 end;

#include "MtxExpr.hpp" #include "Math387.hpp" #include "Optimization.hpp" double __fastcall Banana(TVec* const Parameters, TVec* const Constants, System::TObject* const * ObjConst, const int ObjConst_Size) { double* Pars = Parameters->PValues1D(0); return 100.0*IntPower(Pars[1] - IntPower(Pars[0],2),2) + IntPower(1.0 - Pars[0],2); } void __fastcall Example(); { double Pars[2]; double fmin; TOptStopReason StopReason; // initial estimates for x1 and x2 Pars[0] = 0; Pars[1] = 0; int iters = Simplex(Banana,Pars,1,NULL,-1,NULL,-1,fmin,StopReason,mvDouble,1000,1.0E-8,NULL); // stop if Iters >1000 or Tolerance < 1e-8 // Returns Pars = [1,1] and FMin = 0, meaning x1=1, x2=1 and minimum value is 0 }

Optimization, Functions, Example, See Also

What do you think about this topic? Send feedback!