無約束優(yōu)化搜索方法鮑威爾法

1、無約束優(yōu)化搜索方法上機(jī)實(shí)踐報(bào)告1、寫出所選擇的無約束優(yōu)化搜索算法的基本過程、原理（可附流程圖說明）鮑威爾（Powell ）法是直接利用函數(shù)值來構(gòu)造共軛方向的一種方法 在鮑威爾基本算法中，每一輪迭代都用連結(jié)始點(diǎn)和終點(diǎn)所產(chǎn)生出的搜 索方向去替換原向量組中的第一個(gè)向量，而不管它的“好壞”，這是產(chǎn)生向量組線性相關(guān)的原因所在。在改進(jìn)的算法中首先判斷原向量組是否需要替換。如果需要替換，還要進(jìn)一步判斷原向量組中哪個(gè)向量最壞，然后再用新產(chǎn)生的向量替換 這個(gè)最壞的向量，以保證逐次生成共軛方向。2、程序計(jì)算結(jié)果分析：中間各步驟的結(jié)果分析及與理論計(jì)算結(jié)果分析對比。 算例：ff=x0*x0+2*x1*x1-4*x0-

2、2*x0*x1;(1 )鮑威爾改進(jìn)算法 C+ 程序清單：#include "stdio.h"#include "stdlib.h"#include "math.h"double objf(double x)double ff;ff=x0*x0+2*x1*x1-4*x0-2*x0*x1;return(ff);void jtf(double x0 ,double h0,double s ,intn,double a ,double b )int i;double *x3,h,f1,f2,f3;for (i=0;i<3;i+)xi=(

3、double *)malloc (n*sizeof(double);h=h0;for(i=0;i<n;i+)*(x0+i)=x0i;f1=objf(x0);for(i=0;i<n;i+)*(x1+i)=*(x0+i)+h*si;f2=objf(x1);if(f2>=f1)h= -h0;for (i=0;i<n;i+)*(x2+i)=*(x0+i);f3=f1;for(i=0;i<n;i+)*(x0+i)= *(x1+i);*(x1+i)= *(x2+i);f1=f2;f2=f3;for(;)h=2. *h;for(i=0;i<n;i+)*(x2+i)=* (

4、x1+i) +h*si;f3= objf(x2);if(f2<f3)break;else for(i=0;i<n;i+)*(x0+i)= *(x1+i);*(x1+i)= *(x2+i);f1=f2;f2=f3;if(h<0. )for(i=0;i<n;i+)ai=*(x2+i);bi=*(x0+i);elsefor(i=0;i<n;i+)ai=*(x0+i);bi=*(x2+i);for(i=0;i<3;i+)free(xi);double gold(double a,double b,double eps,int n,double xx) int i;d

5、ouble f1,f2,*x2,ff,q,w; for(i=0;i<2;i+)xi=(double*)malloc (n*sizeof(double); for(i=0;i<n;i+)*(x0+i)=ai+0.618*(bi-ai); *(x1+i)=ai+0.382*(bi-ai);f1=objf(x0);f2=objf(x1);doif(f1>f2)for(i=0;i<n;i+)bi=*(x0+i);*(x0+i)=*(x1+i);f1=f2;*(x1+i)=ai+0.382*(bi-ai);f2=objf(x1);elsefor(i=0;i<n;i+)ai=

6、*(x1+i);*(x1+i)=*(x0+i);f2=f1;for(i=0;i<n;i+)*(x0+i)=ai+0.618*(bi-ai); f1=objf(x0);q=0;for(i=0;i<n;i+)q=q+(bi-ai)*(bi-ai);w=sqrt(q);while(w>eps);for(i=0;i<n;i+)xxi=0.5*(ai+bi);ff=objf(xx);free(xi);return(ff);double oneoptim(double x0,double s,double h0,double n,double x)double *a,*b,ff;a

7、=(double *)malloc(n*sizeof(double);b=(double *)malloc(n*sizeof(double);jtf(x0,h0,s,n,a,b);ff=gold(a,b,epsg,n,x);free(a);free(b);return(ff);double powell(double p,double h0,double eps,double n,double x)int i,j,m;double *xx4,*ss,*s;double f,f0,f1,f2,f3,fx,dlt,df,sdx,q,d;ss=(double *)malloc(n*(n+1)*siz

8、eof(double);epsg,intepsg,ints=(double *)malloc(n*sizeof(double);for (j=0;j<=n;j+)*(ss+i*(n+1)+j)=0;*(ss+i*(n+1)+i)=1;for (i=0;i<4;i+)xxi=(double *)malloc(n*sizeof(double);for (i=0;i<n;i+)*(xx0+i)=pi;for(;)for (i=0;i<n;i+)*(xx1+i)=*(xx0+i);xi=*(xx1+i);f0=f1=objf(x);dlt=-1;for (j=0;j<n;

9、j+)for (i=0;i<n;i+)*(xx0+i)=xi;*(s+i)=*(ss+i*(n+1)+j);f=oneoptim(xx0,s,h0,epsg,n,x);df=f0-f;if(df>dlt)dlt=df;m=j;sdx=0.;for (i=0;i<n;i+)sdx=sdx+fabs(xi-(*(xx1+i);if(sdx<eps)free(ss);free(s);for (i=0;i<4;i+)free(xxi);return(f);for (i=0;i<n;i+)*(xx2+i)=xi;f2=f;for (i=0;i<n;i+)*(xx

10、3+i)=2.*(*(xx2+i)-(*(xx1+i);xi=*(xx3+i);fx=objf(x);f3=fx;q=(f1-2*f2+f3)*(f1-f2-dlt)*(f1-f2-dlt);d=0.5*dlt*(f1-f3)*(f1-f3);if(f3<f1)|(q<d)if(f2<=f3)for (i=0;i<n;i+)*(xx0+i)=*(xx2+i);elsefor (i=0;i<n;i+)*(xx0+i)=*(xx3+i);elsefor (i=0;i<n;i+)*(ss+(i+1)*(n+1)=xi-(*(xx1+i);*(s+i)=*(ss+(

11、i+1)*(n+1);f=oneoptim(xx0,s,h0,epsg,n,x);for(i=0;i<n;i+)*(xx0+i)=xi;for (j=m+1;j<=n;j+)*(ss+i*(n+1)+j-1)=*(ss+i*(n+1)+j);void main()double p=1,1;double ff,x2,x1,x2,f;ff=powell(p,0.3,0.001,0.0001,2,x); printf("shuchuzuiyoujie ：n"); x1=x1;x2=x2;f=ff;printf("x1=%f,x2=%f,f=%fn",x1,x2,f);getchar();(2)運(yùn)行結(jié)果為：算例 1ff=x0*x0+x1*x1+x0+x0*x1輸出結(jié)果：shuchuzuiyoujie u|x1=