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声振论坛»论坛 › 算法编程 › Matlab讨论区 › 一些简单最优化方法的matlab实现
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[共享资源] 一些简单最优化方法的matlab实现

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happy
发表于 2006-11-17 10:07 | 显示全部楼层 |阅读模式

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x
  1. clear;
  2. A=[2,1,4,0;2,2,0,4];
  3. B=[2,3];
  4. C=[12,8,16,12];
  5. f=y(A,B,C)
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  1. %对偶单纯形法
  2. function result=y(A,B,C)
  3. a=-1*A;
  4. [row line]=size(A);
  5. a=[a eye(row,row)];
  6. b=-1*B;
  7. c=[C zeros(1,row)];
  8. dex=c;                                                %dex为判别数                          
  9. basic=line+1:1;line+row;                              %basic为基可行解
  10. X=zeros(1,line);
  11. X1=zeros(1,line+row);
  12. b1=sort(b);
  13. while(b1(1)<0)
  14.     m=0;   
  15.     for i=1:length(b)
  16.         if(b(i)<m)
  17.             m=b(i);   j=i;                            %求出最小的b
  18.         end
  19.     end;   
  20.    n=a(j,:);
  21.    count=0;
  22.    for i=1:length(n)
  23.        if(n(i)>=0)   
  24.            count=count+1;
  25.        end
  26.    end;
  27.    if(count==length(n))   
  28.        error('无最优解');
  29.    end
  30.    seta=dex./n;
  31.    seta1=-Inf;
  32.    for i=1:length(seta)
  33.       if(seta(i)>=seta1&n(i)<0)                    %求出最大且为负的seta
  34.              seta1=seta(i);   k=i;
  35.       end
  36.    end;   
  37.    basic(j)=k;
  38.    b(j)=b(j)/a(j,k);
  39.    a(j,:)=a(j,:)/a(j,k);
  40.    for i=1:length(b)
  41.        if(i~=j)
  42.            b(i)=b(i)-b(j)*a(i,k);
  43.            a(i,:)=a(i,:)-a(j,:)*a(i,k);
  44.        end   
  45.    end;
  46.   q=dex(k);
  47.   dex=dex-q*a(j,:);
  48.   b1=sort(b);
  49. end;
  50. for i=1:length(basic)
  51.     temp=basic(i);
  52.     X1(temp)=b(i);
  53. end;
  54. for i=1:length(X)
  55.     X(i)=X1(i);
  56. end;
  57. X=X'
  58. X1=X1';
  59. result=c*X1;
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happy
 楼主| 发表于 2006-11-17 10:08 | 显示全部楼层
  1. %不精确一维搜索法
  2. function result=Usearch2(f,x1,x2,df,x0,p)
  3. mu=0.4;sgma=0.8;a=0;b=inf;arf=1;m_count=0;s_count=0;
  4. pk=p;
  5. x3=x0;
  6. x4=x3+arf*pk;m_count=m_count+2;s_count=s_count+2;
  7. f1=subs(f,{x1,x2},{x3(1,1),x3(2,1)});m_count=m_count+4;s_count=s_count+3;
  8. f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});m_count=m_count+4;s_count=s_count+3;
  9. gk1=subs(df,{x1,x2},{x3(1,1),x3(2,1)});m_count=m_count+7;s_count=s_count+4;
  10. gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});m_count=m_count+7;s_count=s_count+4;
  11. while (f1-f2<=-mu*arf*gk1'*pk)
  12.    b=arf;arf=(a+arf)/2;x4=x3+arf*pk;f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});
  13.    m_count=m_count+19;s_count=s_count+12;
  14. end;
  15. m_count=m_count+5;s_count=s_count+2;
  16. while (1>0)
  17.     if(gk2'*pk<sgma*gk1'*pk)
  18.         a=arf;a=min(2*arf,(a+b)/2);x4=x3+arf*pk;f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});
  19.         m_count=m_count+21;s_count=s_count+12;
  20.     while (f1-f2<=-mu*arf*gk1'*pk)
  21.         b=arf;arf=(a+arf)/2;x4=x3+arf*pk;f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});
  22.         m_count=m_count+19;s_count=s_count+12;
  23.     end;
  24.     m_count=m_count+5;s_count=s_count+2;
  25.     else
  26.         break;
  27.     end
  28. end;
  29. result=[arf,m_count,s_count];
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happy
 楼主| 发表于 2006-11-17 10:08 | 显示全部楼层
  1. %不精确一维搜索法
  2. function result=Usearch1(f,x1,x2,df,x0,p)
  3. mu=0.001;sgma=0.99;a=0;b=inf;arf=1;m_count=0;s_count=0;
  4. pk=p;
  5. x3=x0;
  6. x4=x3+arf*pk;m_count=m_count+2;s_count=s_count+2;
  7. f1=subs(f,{x1,x2},{x3(1,1),x3(2,1)});m_count=m_count+4;s_count=s_count+3;
  8. f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});m_count=m_count+4;s_count=s_count+3;
  9. gk1=subs(df,{x1,x2},{x3(1,1),x3(2,1)});m_count=m_count+7;s_count=s_count+4;
  10. gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});m_count=m_count+7;s_count=s_count+4;
  11. while (f1-f2<=-mu*arf*gk1'*pk)
  12.    b=arf;arf=(a+arf)/2;x4=x3+arf*pk;f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});
  13.    m_count=m_count+19;s_count=s_count+12;
  14. end;
  15. m_count=m_count+5;s_count=s_count+2;
  16. while (1>0)
  17.     if(gk2'*pk<sgma*gk1'*pk)
  18.         a=arf;a=min(2*arf,(a+b)/2);x4=x3+arf*pk;f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});
  19.         m_count=m_count+21;s_count=s_count+12;
  20.     while (f1-f2<=-mu*arf*gk1'*pk)
  21.         b=arf;arf=(a+arf)/2;x4=x3+arf*pk;f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});
  22.         m_count=m_count+19;s_count=s_count+12;
  23.     end;
  24.     m_count=m_count+5;s_count=s_count+2;
  25.     else
  26.         break;
  27.     end
  28. end;
  29. result=[arf,m_count,s_count];
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happy
 楼主| 发表于 2006-11-17 10:09 | 显示全部楼层
  1. %精确一维搜索
  2. function result=Asearch(y,ar,b1)
  3. a=0;b=b1;e=1e-5;a1=a+0.382*(b-a);f1=subs(y,{ar},{a1});a2=a+0.618*(b-a);f2=subs(y,{ar},{a2});M_count=0;S_count=0;
  4. M_count=M_count+30;S_count=S_count+12;
  5. while abs(b-a)>=e
  6.           if f1<f2
  7.              b=a2;a2=a1;f2=f1;a1=a+0.382*(b-a);f1=subs(y,{ar},{a1});M_count=M_count+15;S_count=S_count+6;
  8.           else
  9.              a=a1;a1=a2;f1=f2;a2=a+0.618*(b-a);f2=subs(y,{ar},{a2});M_count=M_count+15;S_count=S_count+6;
  10.           end
  11.           S_count=S_count+1;
  12. end;
  13. answer=0.5*(a+b);
  14. M_count=M_count+1;S_count=S_count+1;
  15. result=[answer,M_count,S_count];
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 楼主| 发表于 2006-11-17 10:09 | 显示全部楼层
  1. %BFGS计算算法(不精确一维搜索,k=21,mul_count=2380,sum_count=1448,花费时间很少)
  2. syms x1 x2;
  3. f=50*(x2-x1^2)^2+(1-x1)^2;
  4. v=[x1,x2];
  5. df=jacobian(f,v);
  6. df=df.';
  7. epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;H0=[1,0;0,1];mul_count=0;sum_count=0;
  8. mul_count=mul_count+7;sum_count=sum_count+4;
  9. while(norm(g1)>epson&k<300)
  10.     mul_count=mul_count+2;sum_count=sum_count+1;
  11.     if k==0
  12.          p=-H0*g1;mul_count=mul_count+4;sum_count=sum_count+2;
  13.     else
  14.         w1=sqrt(yk'*H0*yk)*((sk/(yk'*sk)-H0*yk/(yk'*H0*yk)));mul_count=mul_count+22;sum_count=sum_count+10;
  15.         H1=H0-H0*yk*yk'*H0/(yk'*H0*yk)+sk*sk'/(yk'*sk)+w1*w1';mul_count=mul_count+40;sum_count=sum_count+22;
  16.         p=-H1*g1;mul_count=mul_count+4;sum_count=sum_count+2;
  17.         H0=H1;
  18.     end
  19.     x00=x0;
  20.     result=Usearch1(f,x1,x2,df,x0,p);
  21.     arf=result(1);Mul=result(2);Sum=result(3);
  22.     mul_count=mul_count+Mul;sum_count=sum_count+Sum;
  23.     x0=x0+arf*p;
  24.     g0=g1;
  25.     g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
  26.     p0=p;
  27.     yk=g1-g0; sk=x0-x00;
  28.     k=k+1;
  29.     mul_count=mul_count+9;sum_count=sum_count+11;
  30. end;
  31. k
  32. x0
  33. mul_count
  34. sum_count
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 楼主| 发表于 2006-11-17 10:10 | 显示全部楼层
  1. %BFGS计算算法(精确一维搜索,k=16,mul_count=8888,sum_count=4227,花费时间很少)
  2. syms x1 x2 ar;
  3. f=50*(x2-x1^2)^2+(1-x1)^2;
  4. v=[x1,x2];
  5. df=jacobian(f,v);
  6. df=df.';
  7. epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;H0=[1,0;0,1];mul_count=0;sum_count=0;
  8. mul_count=mul_count+7;sum_count=sum_count+4;
  9. while(norm(g1)>epson)
  10.     mul_count=mul_count+2;sum_count=sum_count+1;
  11.     if k==0
  12.          p=-H0*g1;mul_count=mul_count+4;sum_count=sum_count+2;
  13.     else
  14.         w1=sqrt(yk'*H0*yk)*((sk/(yk'*sk)-H0*yk/(yk'*H0*yk)));mul_count=mul_count+22;sum_count=sum_count+10;
  15.         H1=H0-H0*yk*yk'*H0/(yk'*H0*yk)+sk*sk'/(yk'*sk)+w1*w1';mul_count=mul_count+40;sum_count=sum_count+22;
  16.         p=-H1*g1;mul_count=mul_count+4;sum_count=sum_count+2;
  17.         H0=H1;
  18.     end
  19.     x00=x0;
  20.     y=subs(f,{x1,x2},{x0(1,1)+ar*p(1,1),x0(2,1)+ar*p(2,1)});mul_count=mul_count+18;sum_count=sum_count+12;
  21.     result1=qujian(y,ar);
  22.     b1=result1(1);mul_count=mul_count+result1(2);sum_count=sum_count+result1(3);
  23.     result2=Asearch(y,ar,b1);
  24.     arf=result2(1);mul_count=mul_count+result2(2);sum_count=sum_count+result2(3);
  25.     x0=x0+arf*p;
  26.     g0=g1;
  27.     g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
  28.     p0=p;
  29.     yk=g1-g0; sk=x0-x00;
  30.     k=k+1;
  31.     mul_count=mul_count+9;sum_count=sum_count+11;
  32. end;
  33. k
  34. x0
  35. mul_count
  36. sum_count
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happy
 楼主| 发表于 2006-11-17 10:10 | 显示全部楼层
  1. %最速下降法(不精确一维搜索,k＝1000,花费时间太多,精度远不能达到要求)
  2. syms x1 x2;
  3. f=50*(x2-x1^2)^2+(1-x1)^2;
  4. v=[x1,x2];
  5. df=jacobian(f,v);
  6. df=df.';
  7. epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;mul_count=0;sum_count=0;
  8. mul_count=mul_count+7;sum_count=sum_count+4;
  9. while(norm(g1)>epson&k<1000)
  10.     mul_count=mul_count+2;sum_count=sum_count+1;
  11.     p=-g1;
  12.     result=Usearch1(f,x1,x2,df,x0,p);
  13.     arf=result(1);Mul=result(2);Sum=result(3);
  14.     mul_count=mul_count+Mul;sum_count=sum_count+Sum;
  15.     x0=x0+arf*p;
  16.     g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
  17.     k=k+1;
  18.     mul_count=mul_count+9;sum_count=sum_count+7;
  19. end;
  20. k
  21. x0
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happy
 楼主| 发表于 2006-11-17 10:10 | 显示全部楼层
  1. %最速下降法(精确一维搜索,k=1000,花费时间太多,精度远不能达到要求)
  2. syms x1 x2 ar;
  3. f=50*(x2-x1^2)^2+(1-x1)^2;
  4. v=[x1,x2];
  5. df=jacobian(f,v);
  6. df=df.';
  7. epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;mul_count=0;sum_count=0;
  8. mul_count=mul_count+7;sum_count=sum_count+4;
  9. while(norm(g1)>epson&k<1000)
  10.     mul_count=mul_count+2;sum_count=sum_count+1;
  11.     p=-g1;
  12.     y=subs(f,{x1,x2},{x0(1,1)+ar*p(1,1),x0(2,1)+ar*p(2,1)});mul_count=mul_count+18;sum_count=sum_count+12;
  13.     result1=qujian(y,ar);
  14.     b1=result1(1);mul_count=mul_count+result1(2);sum_count=sum_count+result1(3);
  15.     result2=Asearch(y,ar,b1);
  16.     arf=result2(1);mul_count=mul_count+result2(2);sum_count=sum_count+result2(3);
  17.     x0=x0+arf*p;
  18.     g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
  19.     k=k+1;
  20.     mul_count=mul_count+9;sum_count=sum_count+7;
  21. end;
  22. k
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 楼主| 发表于 2006-11-17 10:10 | 显示全部楼层
  1. %阻尼Newton算法(k=2,mul_count=44,sum_count=28,最少迭代)
  2. syms x1 x2;
  3. f=50*(x2-x1^2)^2+(1-x1)^2;
  4. v=[x1,x2];
  5. df=jacobian(f,v);
  6. df=df.';
  7. G=jacobian(df,v);
  8. epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});G1=subs(G,{x1,x2},{x0(1,1),x0(2,1)});k=0;mul_count=0;sum_count=0;
  9. mul_count=mul_count+12;sum_count=sum_count+6;
  10. while(norm(g1)>epson)
  11.     p=-G1\g1;
  12.     x0=x0+p;
  13.     g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
  14.     G1=subs(G,{x1,x2},{x0(1,1),x0(2,1)});
  15.     k=k+1;
  16.     mul_count=mul_count+16;sum_count=sum_count+11;
  17. end;
  18. k
  19. x0
  20. mul_count
  21. sum_count
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 楼主| 发表于 2006-11-17 10:11 | 显示全部楼层
  1. %进退法
  2. function result=qujian(y,ar)
  3. t0=0; dex=1;M_count=0;S_count=0;
  4. t1=t0+dex;S_count=S_count+1;
  5. ft0=subs(y,{ar},{t0});M_count=M_count+14;S_count=S_count+4;
  6. ft1=subs(y,{ar},{t1});M_count=M_count+14;S_count=S_count+4;
  7. if(ft1<=ft0)
  8.     dex=2*dex;t2=t1+dex;ft2=subs(y,{ar},{t2});M_count=M_count+15;S_count=S_count+5;
  9.     while(ft1>ft2)
  10.         t1=t2;dex=2*dex;t2=t1+dex;ft1=subs(y,{ar},{t1});ft2=subs(y,{ar},{t2});M_count=M_count+29;S_count=S_count+9;
  11.     end
  12. else
  13.         dex=dex/2;t2=t1;t1=t2-dex;ft1=subs(y,{ar},{t1});M_count=M_count+15;S_count=S_count+5;
  14.     while(ft1>ft0)
  15.         dex=dex/2;t2=t1;t1=t2-dex;ft1=subs(y,{ar},{t1});M_count=M_count+15;S_count=S_count+5;
  16.     end
  17. end
  18. result=[t2,M_count,S_count];
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 楼主| 发表于 2006-11-17 10:11 | 显示全部楼层
  1. %PRP直接计算算法(不精确一维搜索,k=83,mul_count=19842,sum_count=12722时间略长)
  2. syms x1 x2;
  3. f=50*(x2-x1^2)^2+(1-x1)^2;
  4. v=[x1,x2];
  5. df=jacobian(f,v);
  6. df=df.';
  7. epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;mul_count=0;sum_count=0;
  8. mul_count=mul_count+7;sum_count=sum_count+4;
  9. while(norm(g1)>epson&k<1000)
  10.     mul_count=mul_count+2;sum_count=sum_count+1;
  11.     if k==0
  12.          p=-g1;
  13.     else
  14.         bta=g1'*(g1-g0)/(g0'*g0);
  15.         p=-g1+bta*p0;
  16.         mul_count=mul_count+7;sum_count=sum_count+6;
  17.     end
  18.     result=Usearch2(f,x1,x2,df,x0,p);
  19.     arf=result(1);Mul=result(2);Sum=result(3);
  20.     mul_count=mul_count+Mul;sum_count=sum_count+Sum;
  21.     x0=x0+arf*p;
  22.     g0=g1;
  23.     g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
  24.     p0=p;
  25.     k=k+1;
  26.     mul_count=mul_count+9;sum_count=sum_count+7;
  27. end;
  28. k
  29. x0
  30. mul_count
  31. sum_count
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happy
 楼主| 发表于 2006-11-17 10:11 | 显示全部楼层
  1. %PRP重新开始计算算法(不精确一维搜索,k=133,mul_count=18421,sum_count=11850时间略长)
  2. syms x1 x2;
  3. f=50*(x2-x1^2)^2+(1-x1)^2;
  4. v=[x1,x2];
  5. df=jacobian(f,v);
  6. df=df.';
  7. epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;mul_count=0;sum_count=0;
  8. mul_count=mul_count+7;sum_count=sum_count+4;
  9. while(norm(g1)>epson&k<1000)
  10.     mul_count=mul_count+2;sum_count=sum_count+1;
  11.     if k==0
  12.          p=-g1;
  13.     else
  14.         bta=g1'*(g1-g0)/(g0'*g0); mul_count=mul_count+5;sum_count=sum_count+4;
  15.         if(mod(k,2))
  16.                p=-g1+bta*p0; mul_count=mul_count+3;sum_count=sum_count+2;
  17.         else
  18.                p=-g1;
  19.         end
  20.     end
  21.     result=Usearch2(f,x1,x2,df,x0,p);
  22.     arf=result(1);Mul=result(2);Sum=result(3);
  23.     mul_count=mul_count+Mul;sum_count=sum_count+Sum;
  24.     x0=x0+arf*p;
  25.     g0=g1;
  26.     g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
  27.     p0=p;
  28.     k=k+1;
  29.     mul_count=mul_count+9;sum_count=sum_count+7;
  30. end;
  31. k
  32. x0
  33. mul_count
  34. sum_count
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happy
 楼主| 发表于 2006-11-17 10:11 | 显示全部楼层
  1. %PRP直接计算降法(精确一维搜索,k=19,mul_count=8390,sum_count=3745,花费时间很少)
  2. syms x1 x2 ar;
  3. f=50*(x2-x1^2)^2+(1-x1)^2;
  4. v=[x1,x2];
  5. df=jacobian(f,v);
  6. df=df.';
  7. epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;mul_count=0;sum_count=0;
  8. mul_count=mul_count+7;sum_count=sum_count+4;
  9. while(norm(g1)>epson)
  10.     mul_count=mul_count+2;sum_count=sum_count+1;
  11.     if k==0
  12.          p=-g1;
  13.     else
  14.         bta=(g1'*(g1-g0))/(g0'*g0);
  15.         p=-g1+bta*p0;
  16.         mul_count=mul_count+7;sum_count=sum_count+6;
  17.     end
  18.     y=subs(f,{x1,x2},{x0(1,1)+ar*p(1,1),x0(2,1)+ar*p(2,1)});mul_count=mul_count+18;sum_count=sum_count+12;
  19.     result1=qujian(y,ar);
  20.     b1=result1(1);mul_count=mul_count+result1(2);sum_count=sum_count+result1(3);
  21.     result2=Asearch(y,ar,b1);
  22.     arf=result2(1);mul_count=mul_count+result2(2);sum_count=sum_count+result2(3);
  23.     x0=x0+arf*p;
  24.     g0=g1;
  25.     g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
  26.     p0=p;
  27.     k=k+1;
  28.     mul_count=mul_count+9;sum_count=sum_count+7;
  29. end;
  30. k
  31. x0
  32. mul_count
  33. sum_count
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happy
 楼主| 发表于 2006-11-17 10:12 | 显示全部楼层
  1. %PRP重新开始计算算法(精确一维搜索,k=21,mul_count=9901,sum_count=4470,花费时间很少)
  2. syms x1 x2;
  3. f=50*(x2-x1^2)^2+(1-x1)^2;
  4. v=[x1,x2];
  5. df=jacobian(f,v);
  6. df=df.';
  7. epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;mul_count=0;sum_count=0;
  8. mul_count=mul_count+7;sum_count=sum_count+4;
  9. while(norm(g1)>epson)
  10.     mul_count=mul_count+2;sum_count=sum_count+1;
  11.     if k==0
  12.          p=-g1;
  13.     else
  14.         bta=g1'*(g1-g0)/(g0'*g0); mul_count=mul_count+5;sum_count=sum_count+4;
  15.         if(mod(k,2))
  16.                p=-g1+bta*p0; mul_count=mul_count+3;sum_count=sum_count+2;
  17.         else
  18.                p=-g1;
  19.         end
  20.     end
  21.     y=subs(f,{x1,x2},{x0(1,1)+ar*p(1,1),x0(2,1)+ar*p(2,1)});mul_count=mul_count+18;sum_count=sum_count+12;
  22.     result1=qujian(y,ar);
  23.     b1=result1(1);mul_count=mul_count+result1(2);sum_count=sum_count+result1(3);
  24.     result2=Asearch(y,ar,b1);
  25.     arf=result2(1);mul_count=mul_count+result2(2);sum_count=sum_count+result2(3);
  26.     x0=x0+arf*p;
  27.     g0=g1;
  28.     g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
  29.     p0=p;
  30.     k=k+1;
  31.     mul_count=mul_count+9;sum_count=sum_count+7;
  32. end;
  33. k
  34. x0
  35. mul_count
  36. sum_count
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happy
 楼主| 发表于 2006-11-17 10:12 | 显示全部楼层
  1. %DFP计算算法(不精确一维搜索,k=27,mul_count=2326,sum_count=1462,花费时间很少)
  2. syms x1 x2;
  3. f=50*(x2-x1^2)^2+(1-x1)^2;
  4. v=[x1,x2];
  5. df=jacobian(f,v);
  6. df=df.';
  7. epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;H0=[1,0;0,1];mul_count=0;sum_count=0;
  8. mul_count=mul_count+7;sum_count=sum_count+4;
  9. while(norm(g1)>epson&k<1000)
  10.     mul_count=mul_count+2;sum_count=sum_count+1;
  11.     if k==0
  12.          p=-H0*g1;mul_count=mul_count+7;sum_count=sum_count+4;
  13.     else
  14.         H1=H0-H0*yk*yk'*H0/(yk'*H0*yk)+sk*sk'/(yk'*sk);mul_count=mul_count+36;sum_count=sum_count+18;
  15.         p=-H1*g1;mul_count=mul_count+7;sum_count=sum_count+4;
  16.         H0=H1;
  17.     end
  18.     x00=x0;
  19.     result=Usearch1(f,x1,x2,df,x0,p);
  20.     arf=result(1);Mul=result(2);Sum=result(3);
  21.     mul_count=mul_count+Mul;sum_count=sum_count+Sum;
  22.     x0=x0+arf*p;
  23.     g0=g1;
  24.     g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
  25.     p0=p;
  26.     yk=g1-g0; sk=x0-x00;
  27.     k=k+1;
  28.     mul_count=mul_count+9;sum_count=sum_count+11;
  29. end;
  30. k
  31. x0
  32. mul_count
  33. sum_count
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