MinBrent Routines

Summary

Minimizes single variable function.

Declaration

Function MinBrent(ax, bx: TSample; Func: TRealFunction; const Consts: array of TSample; const ObjConst: array of TObject; out MinX: TSample): Integer;

Declaration

Function MinBrent(ax, bx: TSample; Func: TRealFunction; const Consts: array of TSample; const ObjConst: array of TObject; out MinX: TSample; MaxIter: integer; Accuracy: TSample = 1.0E-8; Verbose: TStrings = nil): Integer;

Parameter	Description
ax,bx	Set ax and bx to define initial interval for minimum.
Func	Real function of single variable (must be of TRealFunction type) to be minimized.
Consts,PConsts	Additional Fun constant parameteres (can be/is usually nil).
MinX	Returns the position of function minimum.
MaxIter	Maximum allowed numer of minimum search iterations.
Accuracy	Desired minimum position tolerance.
Verbose	If assigned, stores Func, evaluated at each iteration step.

Result

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

Description

Minimizes the function of one variable. This routine uses slightly modified version of the algol 60 procedure localmin, introduced by Richard Brent.

See Also
TRealFunction

Example 1

Problem: Find the minimum of the function of single variable by using the Brent method.
Solution: The function is defined by the following equation:

    Uses MtxVec, Math387, Optimization;
    function Fun(Pars: TVec: Const Consts: Array of TSample;
    Const ObjConsts: Array of TObject): TSample;
    begin
      Result := Sin(Pars[0])+Sqr(Pars[0]+2);
	    // note that Pars holds only one variable !
    end;
    procedure Example;
    var Res,x : TSample;
    begin
      // initial estimates for x1 and x2
      Res := MinBrent(-10,10,Fun,[],[],x,500,1e-8);
      // stop if Iters >500 or Tolerance < 1e-8
	    // Returns Res = -1.8582461797
    end;

    #include "MtxVecCpp.h" //MtxVecCPP.cpp must be included in the project
    #include "Math387.hpp"
    #include "Optimization.hpp"
    double __fastcall Fun(TVec * x, double const * c, const int c_Size, System::TObject* const * o, const int o_Size)
    {
      double* X = x->PValues(0);
      
    	return Sin(X[0])+IntPower(X[0]+2,2);
    	// note that Pars holds only one variable !
    }
    void __fastcall Example();
    {
      // initial estimates for x1 and x2
      double x;
	    int iter = MinBrent(-10,10,Fun,NULL,-1,NULL,-1,x,500,1.0E-8,NULL);
      // stop if Iters >500 or Tolerance < 1e-8
	    // returns res = -1.8582461797
    }

    private double Fun(TVec pars, double[] c, object[] o)
    {
      return Math.Sin(Pars[0])+Math387.IntPower(Pars[0]+2,2);
	    // note that Pars holds only one variable !
    }
    private void Example()
    {
      // initial estimates for x1 and x2
      double x;
      double res = Optimization.MinBrent(-10,10,Fun,null,null,out x, 500,1e-8,null);
      // stop if Iters >500 or Tolerance < 1e-8
	    // Returns res = -1.8582461797
    }