#definen12#definett#definead定義常量//tt

初始迭代步長//ad收斂精度floatia;floatfny(float*x){floatf;f=10*pow((x[0]+x[1]-5),2)+pow((x[0]-x[1]),2);//

目標函數(shù)return(f);}float*iterate(float*x,floata,float*s){float*x1;x1=(float*)malloc(n1*sizeof(float));for(inti=0;i<n1;i++)x1[i]=x[i]+a*s[i];return(x1);}floatfunc(float*x,floata,float*s){float*x1;x1=iterate(x,a,s);floatf=fny(x1);return(f);}voidfinding(floata[3],floatf[3],float*xk,float*s){floatt=tt;floata1,f1;a[0]=0;f[0]=func(xk,a[0],s);for(inti=0;;i++){a[1]=a[0]+t;f[1]=func(xk,a[1],s);if(f[1]<f[0])break;if(fabs(f[1]-f[0])>=ad){t=-t;a[0]=a[1];f[0]=f[1];}else{if(ia==1)return;t=t/2;ia=1;}}for(i=0;;i++){a[2]=a[1]+t;f[2]=func(xk,a[2],s);if(f[2]>f[1])break;t=2*t;a[0]=a[1];f[0]=f[1];a[1]=a[2];f[1]=f[2];}if(a[0]>a[2]){a1=a[0];f1=f[0];a[0]=a[2];f[0]=f[2];a[2]=a1;f[2]=f1;}return;}//secondinsertfloatlagrange(float*xk,float*ft,float*s){floata[3],f[3];floatb,c,d,aa;finding(a,f,xk,s);for(inti=0;;i++){if(ia==1){aa=a[1];*ft=f[1];break;}d=(pow(a[0],2)-pow(a[2],2))*(a[0]-a[1])-(pow(a[0],2)-pow(a[1],2))*(a[0]-a[2]);if(fabs(d)==0)break;c=((f[0]-f[2])*(a[0]-a[1])-(f[0]-f[1])*(a[0]-a[2]))/d;if(fabs(c)==0)break;b=((f[0]-f[1])-c*(pow(a[0],2)-pow(a[1],2)))/(a[0]-a[1]);aa=-b/(2*c);*ft=func(xk,aa,s);if(fabs(aa-a[1])<=ad){if(*ft>f[1])aa=a[1];break;}if(aa>a[1]){if(*ft>f[1]){a[2]=aa;f[2]=*ft;}elseif(*ft<f[1]){a[0]=a[1];a[1]=aa;f[0]=f[1];f[1]=*ft;}elseif(*ft==f[1]){a[2]=aa;a[0]=a[1];f[2]=*ft;f[0]=f[1];a[1]=(a[0]+a[2])/2;f[1]=func(xk,a[1],s);}}else{if(*ft>f[1]){a[0]=aa;f[0]=*ft;}elseif(*ft<f[1]){a[2]=a[1];a[1]=aa;f[2]=f[1];f[1]=*ft;}elseif(*ft==f[1]){a[0]=aa;a[2]=a[1];f[0]=*ft;f[2]=f[1];a[1]=(a[0]+a[2])/2;f[1]=func(xk,a[1],s);}}}if(*ft>f[1]){aa=a[1];*ft=f[1];}return(aa);}float*powell(float*xk){floath[n1][n1],s[n1]={0,0},ff[n1+1]={0,0,0};floatf1,f3,aa;floatdk[n1],*x0,xk1[n1];intm=0,i,j;for(i=0;i<n1;i++){for(j=0;j<n1;j++){h[i][j]=0;if(j==i)h[i][j]=1;}}for(intk=0;;k++){ff[0]=fny(xk);x0=xk;for(i=0;i<n1;i++){for(j=0;j<n1;j++)s[j]=h[i][j];floataa=lagrange(xk,&ff[i+1],s);xk=iterate(xk,aa,s);}for(i=0;i<n1;i++){floata,b;dk[i]=xk[i]-x0[i];xk1[i]=2*xk[i]-x0[i];}floatmax=fabs(ff[1]-ff[0]);for(i=1;i<n1;i++)if(fabs(ff[i+1]-ff[i])>max){max=fabs(ff[i+1]-ff[i]);m=i;}f3=fny(xk1);if((f3<ff[0])&&((ff[0]+f3-2*ff[2])*pow((ff[0]-ff[n1]-max),2)<*max*pow((ff[0]-f3),2))){aa=lagrange(xk,&f1,dk);xk=iterate(xk,aa,dk);for(i=m;i<n1-1;i++)for(j=0;j<n1;j++)h[i][j]=h[i+1][j];for(j=0;j<n1;j++)h[n1-1][j]=dk[j];}else{if(ff[n1]>=f3)xk=xk1;}floatxq=0;for(i=0;i<n1;i++)xq+=pow((xk[i]-x0[i]),2);if(xq<=ad)break;}return(xk);}voidmain( ){floatxk[n1]={0,0};//取初始點float*xx;xx=(float*)malloc(n1*sizeof(float));xx=powell(xk);floatff=fny(xx);cout<<"優(yōu)化的結(jié)果