学步园

理论部分参考《Practical Optimization》中4.4节，代码如下：

OneDimensionalOptimization。h

#ifndef _OneDimensionalOptimization_
#define _OneDimensionalOptimization_
#include <algorithm>
using namespace std;
class OneDimensionalOptimization
{
public:
	//参考《Practical Optimization》中4.4节
	double goldenSectionSearch(double(*p)(double x),double& l, double& u, double& x, double tol = 1e-6);
};
#endif

OneDimensionalOptimization.cpp

#include "OneDimensionalOptimization.h"
double OneDimensionalOptimization::goldenSectionSearch(double(*p)(double x),double& l, double& u,double& x, double tol)
{
	//1)
	double xlk = l;
	double xuk = u;
	//2)
	double I1 = xuk - xlk;
	double K = 1.618034;
	double Ikp1 = I1 / K;
	double xak = xuk - Ikp1;
	double xbk = xlk + Ikp1;
	double fak = p(xak);
	double fbk = p(xbk);
	//3)
	while(true)
	{
		double Ikp2 = Ikp1 / K;
		if(fak >= fbk)
		{
			xlk = xak;
			xuk = xuk;

			xak = xbk;
			xbk = xlk + Ikp2;

			fak = fbk;
			fbk = p(xbk);
		}
		else
		{
			xlk = xlk;
			xuk = xbk;

			xak = xuk - Ikp2;
			xbk = xak;

			fbk = fak;
			fak = p(xak);
		}
		Ikp1 = Ikp2;
		//4)
		if(Ikp2 < tol || xak > xbk)
		{
			if(fak > fbk)
				x = 0.5 * (xbk + xuk);
			if(fak == fbk)
				x = 0.5 * (xak + xbk);
			if(fak < fbk)
				x = 0.5 * (xlk + xak);

			l = xlk;
			u = xuk;
			return p(x);
		} 
	}
}

测试代码主程序：

main.cpp

#include "src\Optimizer\OneDimensionalOptimization.h"

#include <fstream>
using namespace std;

double p(double x)
{
	return -sin(x);
}
int main(int argv, char** argc)
{
	OneDimensionalOptimization* one = new OneDimensionalOptimization();
	double l = 0;
	double u = 2*3.1415926;
	double x;
	double res = one->goldenSectionSearch(p,l,u,x,1e-5);
	return 1;
}

该方法的收敛结果误差较大。