#include"stdio.h"
#include"stdlib.h"
#include"math.h"
double objf(double x[])
{double ff;
ff=x[0]*x[0]+x[1]*x[1]-x[0]*x[1]-10*x[0]-4*x[1]+60;
return(ff);
}
double gold(double a[],double b[],double eps,int n,double xx[]) {int i;
double f1,f2,*x[2],ff,q,w;
for(i=0;i<2;i++)
x[i]=(double*)malloc(n*sizeof(double));
for(i=0;i<n;i++)
{*(x[0]+i)=a[i]+0.618*(b[i]-a[i]);
*(x[1]+i)=a[i]+0.382*(b[i]-a[i]);
}
f1=objf(x[0]);
f2=objf(x[1]);
do
{if(f1>f2)
{for(i=0;i<n;i++)
{b[i]=*(x[0]+i);
*(x[0]+i)=*(x[1]+i);
}
f1=f2;
for(i=0;i<n;i++)
*(x[1]+i)=a[i]+0.382*(b[i]-a[i]);
f2=objf(x[1]);
}
else
{for(i=0;i<n;i++)
{a[i]=*(x[1]+i);
*(x[1]+i)=*(x[0]+i);}
f2=f1;
for(i=0;i<n;i++)
*(x[0]+i)=a[i]+0.618*(b[i]-a[i]);
f1=objf(x[0]);
}
q=0;
for(i=0;i<n;i++)
q=q+(b[i]-a[i])*(b[i]-a[i]);
w=sqrt(q);
}while(w>eps);
for(i=0;i<n;i++)
xx[i]=0.5*(a[i]+b[i]);
ff=objf(xx);
for(i=0;i<2;i++)
free(x[i]);
return(ff);
}
void jtf(double x0[],double h0,double s[],int n,double a[],double b[]) {int i;
double*x[3],h,f1,f2,f3;
for(i=0;i<3;i++)
x[i]=(double*)malloc(n*sizeof(double));
h=h0;
for(i=0;i<n;i++)
*(x[0]+i)=x0[i];
f1=objf(x[0]);
for(i=0;i<n;i++)
*(x[1]+i)=*(x[0]+i)+h*s[i];
f2=objf(x[1]);
if(f2>=f1)
{h=-h0;
for(i=0;i<n;i++)
*(x[2]+i)=*(x[0]+i);
f3=f1;
for(i=0;i<n;i++)
{*(x[0]+i)=*(x[1]+i);
*(x[1]+i)=*(x[2]+i);
}
f1=f2;
f2=f3;
}
for(;;)
{h=2*h;
for(i=0;i<n;i++)
*(x[2]+i)=*(x[1]+i)+h*s[i];
f3=objf(x[2]);
if(f2<f3) break;
else
{for(i=0;i<n;i++)
{*(x[0]+i)=*(x[1]+i);
*(x[1]+i)=*(x[2]+i);
}
f1=f2;
f2=f3;
}
}
if(h<0)
for(i=0;i<n;i++)
{a[i]=*(x[2]+i);
b[i]=*(x[0]+i);
}
else
for(i=0;i<n;i++)
{a[i]=*(x[0]+i);
b[i]=*(x[2]+i);
}
for(i=0;i<3;i++)
free(x[i]);
}
double oneoptim(double x0[],double s[],double h0,double epsg,int n,double x[]) {double*a,*b,ff;
a=(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 epsg,int n,double x[]) {int i,j,m;
double*xx[4],*ss,*s;
double f,f0,f1,f2,f3,fx,dlt,df,sdx,q,d;
ss=(double*)malloc(n*(n+1)*sizeof(double));
s=(double*)malloc(n*sizeof(double));
for(i=0;i<n;i++)
{for(j=0;j<=n;j++)
*(ss+i*(n+1)+j)=0;
*(ss+i*(n+1)+i)=1;
}
for(i=0;i<4;i++)
xx[i]=(double*)malloc(n*sizeof(double));
for(i=0;i<n;i++)
*(xx[0]+i)=p[i];
for(;;)
{for(i=0;i<n;i++)
{*(xx[1]+i)=*(xx[0]+i);
x[i]=*(xx[1]+i);
}
f0=f1=objf(x);
dlt=-1;
for(j=0;j<n;j++)
{for(i=0;i<n;i++)
{*(xx[0]+i)=x[i];
*(s+i)=*(ss+i*(n+1)+j);
}
f=oneoptim(xx[0],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(x[i]-(*(xx[1]+i)));
if(sdx<eps)
{free(ss);
free(s);
for(i=0;i<4;i++)
free(xx[i]);
return(f);
}
for(i=0;i<n;i++)
*(xx[2]+i)=x[i];
f2=f;
for(i=0;i<n;i++)
{*(xx[3]+i)=2*(*(xx[2]+i)-(*(xx[1]+i)));
x[i]=*(xx[3]+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++)
*(xx[0]+i)=*(xx[2]+i);
else
for(i=0;i<n;i++)
*(xx[0]+i)=*(xx[3]+i);
}
else
{for(i=0;i<n;i++)
{*(ss+(i+1)*(n+1))=x[i]-(*(xx[1]+i));
*(s+i)=*(ss+(i+1)*(n+1));
}
f=oneoptim(xx[0],s,h0,epsg,n,x);
for(i=0;i<n;i++)
*(xx[0]+i)=x[i];
for(j=m+1;j<=n;j++)
for(i=0;i<n;i++)
*(ss+i*(n+1)+j-1)=*(ss+i*(n+1)+j);
}
}
}
void main()
{double p[]={1,2};
double ff,x[2];
ff=powell(p,0.3,0.001,0.0001,2,x);
printf("x[0]=%f,x[1]=%f,ff=%f\n",x[0],x[1],ff); getchar();
}。