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1、目 录一、 黄金分割法二、 二次插值法三、 最速下降法（阶梯法）四、 变尺度法五、 鲍威尔法一、黄金分割法#include #include #define r 0.618 #define f(x) x*x+2*x golden(float,float,float); main() float a,b,e;printf(“n 请输入区间和收敛精度请输入区间和收敛精度:a,b,en“);scanf(“%f,%f,%f“,golden(a,b,e); golden(float a,float b,float e) float y1,y2,a1,a2,A,Y;int n=0;a1=b-r*(b-a)
2、;a2=a+r*(b-a);y1=f(a1);y2=f(a2);printf(“黄金分割法的搜索过程黄金分割法的搜索过程:“);do printf(“n %d a=%f,b=%f,a1=%f,a2=%f,y1=%f,y2=%f“,n,a,b,a1,a2,y1,y2);if(y1=y2) a=a1;a1=a2;y1=y2;a2=a+r*(b-a);y2=f(a2); else b=a2;a2=a1;y2=y1;a1=b-r*(b-a);y1=f(a1);n+;while(fabs(b-a)/b)=e|fabs(y2-y1)/y2)=e); A=(a+b)/2; Y=f(A);printf(“n
3、%d a=%f,b=%f,a1=%f,a2=%f“,n,a,b,a1,a2);printf(“n 结果结果:n 极值点及其函数值极值点及其函数值:A=%f,Y=%fn“, A,Y); 二、二次插值法#include“stdio.h“ #include“math.h“ #include“conio.h“ void main() float*area(float a1,float p,float a3);float f(float x);float ar,fr;float a1=10,p=0.01,e=0.000001;float pa3;area(a1,p,pa);a1=pa0;float a2
4、=pa1;float a3=pa2;float f1=f(a1);float f2=f(a2);float f3=f(a3);doar=(a3*a3-a2*a2)*f1+(a1*a1-a3*a3)*f2+(a2*a2-a1*a1)*f3);ar=ar/2/(a3-a2)*f1+(a1-a3)*f2+(a2-a1)*f3);fr=f(ar); if(ara2) if(frf2) a3=ar; f3=fr; else if(frf2) a1=ar; f1=fr; else if(fr=f1) if(fabs(f2-f1)a3) temp=a1; a1=a3; a3=temp; a0=a1;a1=a
5、2;a2=a3; return a;float f(float x)float y=pow(fabs(x-1),1.5)+pow(fabs(x-1),2.7);return y;三、最速下降法#include #include float fun1(float x1,float x2) float a;a=2*x1;return a; float fun2(float x1,float x2) float b;b=50*x2;return b; float fun3(float x1,float x2) float y;y=x1*x1+25*x2*x2; return y; main() fl
6、oat t, e=0.01, x1=0, x2=1, a, b, y, m; a=fun1(x1,x2); b=fun2(x1,x2); m=sqrt(a*a+b*b); while(me) t=(a*a+b*b)/(2*a*a+50*b*b); x1=x1-a*t; x2=x2-b*t;a=fun1(x1,x2); b=fun2(x1,x2); m=sqrt(a*a+b*b); y=fun3(x1,x2); printf(“The min is %f“,y); 四、DFP 变尺度法#include #include #include #include#define tt 0.01 #defi
7、ne ff 1.0e-6 #define ac 1.0e-6 #define ad 1.0e-6 #define n 2double ia;double fny(double *x) double x1=x0,x2=x1;double f; f=x1*x1+2*x2*x2-4*x1-2*x1*x2;return f; double * iterate(double *x,double a,double *s) double *x1; int i; x1=(double *)malloc(n*sizeof(double); for(i=0;i=ad)t=-t;a0=a1;f0=f1;elseif
8、(ia=1) return; /breakt=t/2;ia=1; for(i=0;i+) a2=a1+t;f2=func(xk,a2,s);if(f2f1) break;t=2*t;a0=a1;f0=f1;a1=a2;f1=f2; if(a0a2) a1=a0;f1=f0;a0=a2;f0=f2;a2=a1;f2=f1; return; double lagrange(double *xk,double *ft,double *s) int i; double a3,f3; double b,c,d,aa; finding(a,f,xk,s); for(i=0;i+) if(ia=1) aa=
9、a1; *ft=f1; break; d=(pow(a0,2)-pow(a2,2)*(a0-a1)-(pow(a0,2)-pow(a1,2)*(a0-a2);if(fabs(d)=0) break;c=(f0-f2)*(a0-a1)-(f0-f1)*(a0-a2)/d;if(fabs(c)=0) break;b=(f0-f1)-c*(pow(a0,2)-pow(a1,2)/(a0-a1);aa=-b/(2*c);*ft=func(xk,aa,s);if(fabs(aa-a1)f1) aa=a1;break;if(aaa1)if(*ftf1) a2=aa;f2=*ft;else if(*ftf1
10、) a0=aa;f0=*ft;else if(*ftf1) *ft=f1;aa=a1; return aa; double *gradient(double *xk) double *g,f1,f2,q; int i; g=(double*)malloc(n*sizeof(double);f1=fny(xk);for(i=0;i=ac)if(ib=0) xx=xk1; break; fi=*ft;if(k=n-1) int j;xk=xk1;for(i=0;ifi) *ft=fi; xx=xk;xk=x0;return xx; void main () int k;double *xx,f;d
11、ouble xkn=1,1;xx=bfgs(xk);f=fny(xx);printf(“nnThe Optimal Design Result Is:n“);for(k=0;k=f1)h= -h0;for (i=0;if2) for(i=0;ieps); for(i=0;idlt) dlt=df; m=j; sdx=0.; for (i=0;in;i+) sdx=sdx+fabs(xi-(*(xx1+i); if(sdxeps) free(ss); free(s); for (i=0;i4;i+) free(xxi); return(f); for (i=0;in;i+) *(xx2+i)=x
12、i; f2=f; for (i=0;in;i+) *(xx3+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(f3f1)|(qd) if(f2=f3) for (i=0;in;i+) *(xx0+i)=*(xx2+i); else for (i=0;in;i+) *(xx0+i)=*(xx3+i); else for (i=0;in;i+) *(ss+(i+1)*(n+1)=xi-(*(
13、xx1+i); *(s+i)=*(ss+(i+1)*(n+1); f=oneoptim(xx0,s,h0,epsg,n,x); for(i=0;in;i+) *(xx0+i)=xi; for (j=m+1;j=n;j+) for (i=0;in;i+) *(ss+i*(n+1)+j-1)=*(ss+i*(n+1)+j); void main() double p=1,1; double ff,x2; ff=powell(p,0.3,0.001,0.0001,2,x); printf(“输出最优点及其目标函数值：输出最优点及其目标函数值：n“); printf(“x0=%f,x1=%f,ff=%f“,x0,x1,ff);
