最优化方法一维搜索法C++程序

1、精选优质文档-倾情为你奉上加步探索法#include<iostream>#include<math.h>using namespace std;double fun(double t)return (t*t*t-2*t+1);double max(double a,double b)if(a>b)return a;else return b;double min(double a,double b)if(a>b)return b;else return a;double Addstep(double(*pfun)(double t)int k=0;doubl

2、e t0=0,h=1,r=2,t,a=0,b=0;t=t0+h;doif(fun(t)<fun(t0)h=r*h;t0=t;t=t0+h;k+;elseif(k=0)h=-h;k+; elsea=min(t0,t);b=max(t0,t);return a;return b;while(a=b);cout<<" 探索区间为："<<""<<min(t0,t)<<","<<max(t0,t)<<""<<endl;int main(

3、)Addstep(fun);return 0;对分法#include<iostream>#include<math.h>using namespace std;double fun(double t)return (t*t-3*t);double dfun(double t)return (2*t-3);void Dichotomous(double(*pfun)(double t),double (*pdfun)(double t)int maxflag=1000,k=1;double a=-3,b=5,c,err=0.1,t;doc=(a+b)/2;if(dfun(

4、c)<0)a=c;else if(dfun(c)>0)b=c;elsea=c;b=c;k+;while(fabs(a-b)>err&&k<maxflag);if(k>=maxflag)cout<<endl<<"对分法迭代失败!迭代次数为k="<<k<<endl;elsecout<<endl<<" 对分法迭代成功!迭代次数为k="<<k-1<<endl;cout<<"迭代结果：近似根为root=

5、"<<t<<endl;cout<<" 函数值近似为：f(root)="<<fun(t)<<endl;int main()Dichotomous(fun,dfun);return 0;Newton切线法#include<iostream>#include<math.h>using namespace std;double fun(double t)return (t*t*t-2*t+1);double dfun(double t)return (3*t*t-2);void Newto

6、nIterative(double(*pfun)(double t),double (*pdfun)(double t)int maxflag=1000,k=1;double t0=1,err=0.01,t;dot0=t;t=t0-pfun(t0)/pdfun(t0);k+;while(fabs(t-t0)>err&&k<maxflag);if(k>=maxflag)cout<<endl<<" 牛顿迭代失败!迭代次数为k="<<k<<endl;elsecout<<endl<&

7、lt;" 牛顿迭代成功!迭代次数为k="<<k-1<<endl;cout<<" 迭代结果：近似根为root="<<t<<endl;cout<<" 函数值近似为：f(root)="<<fun(t)<<endl;int main()NewtonIterative(fun,dfun);return 0;黄金分割法#include<iostream>#include<math.h>using namespace std;do

8、uble fun(double t)return (t*t+2*t);void Goldensection(double(*pfun)(double t)int maxflag=1000,k=1;double a=-3,b=5,err=0.001,t,t1,t2;dot1=a+0.618*(b-a);t2=b-0.618*(b-a);if(t1=t2)a=t2;b=t1;else if(t1<t2)a=t2; elseb=t1;k+;while(fabs(a-b)>err&&k<maxflag);if(k>=maxflag)cout<<end

9、l<<"黄金分割法迭代失败!迭代次数为k="<<k<<endl;elset=(a+b)/2;cout<<endl<<" 黄金分割法迭代成功!迭代次数为k="<<k-1<<endl;cout<<" 迭代结果：近似根为root="<<t<<endl;cout<<" 函数值近似为：f(root)="<<fun(t)<<endl;int main()Goldensect

10、ion(fun);return 0;抛物线插值法#include<iostream>#include<math.h>using namespace std;double fun(double x)return (8*x*x*x-2*x*x-7*x+3);double max(double a,double b)if(a>b)return a;else return b;double min(double a,double b)if(a>b)return b;else return a;void Parainterpolation(double(*pfun)(

11、double x)double a=0,b=2,err=0.001,x=0,x0=1,f,f0;dox=(x0*x0-b*b)*fun(a)+(b*b-a*a)*fun(x0)+(a*a-x0*x0)*fun(b)/(2*(x0-b)*fun(a)+(b-a)*fun(x0)+(a-x0)*fun(b);f0=fun(x0);f=fun(x);if(f=f0)a=min(x,x0);b=max(x,x0);x0=(a+b)/2;else if(fun(x)-f0)*(x-x0)>0)b=max(x,x0);x0=min(x,x0); elsea=min(x,x0);x0=max(x,x0);while(fabs(x-x0)>err);x=(x+x0)/2;cou