最优化计算的牛顿法＋共轭梯度法的MATLAB程序

suffer

共包含五个 m文件

main.m

1. function y=main(x)
   
2. %This program uses the steepest_down + conjugate_grad method
   
3. %to calculate the minimum of the function f(x)=x(1)^2+2*x(2)^2
   
4. 
   
5. format long
   
6. eps=input('please input your accuracy:');
   
7. %eps is the demmanded accuracy on the norm of
   
8. %the gradient of the objective function
   
9. 
   
10. m=1;
    
11. %m is the count of the iteration step of the algorithm
    
12. 
    
13. iterstep(1,:)=x;
    
14. %iterstep contains the intermediate points of iteration
    
15. 
    
16. while m<=3
    
17.    while norm(gradobject1(x))>eps
    
18.      grad=gradobject1(x);
    
19.      alpha=goldsplictobj(x);
    
20.      x=x-alpha*grad;
    
21.      iterstep(m+1,:)=x;
    
22.      m=m+1;
    
23.   end
    
24. end
    
25. 
    
26. while norm(gradobject1(x))>eps
    
27.     x1=iterstep(m-1,:);
    
28.     x2=iterstep(m,:);
    
29.     grad1=gradobject1(x1);
    
30.     grad2=gradobject1(x2);
    
31.     beta=(norm(gradobject1(x2))/norm(gradobject1(x1)))^2;
    
32.     S=-grad2-beta*grad1;
    
33.     x2=x2-alpha*S;
    
34.     x=x2;
    
35.     iterstep(m+1,:)=x;
    
36.     m=m+1;
    
37. end
    
38. 
    
39. 
    
40. step=max(size(iterstep))-1
    
41. x
    
42. iterstep
    
43. plot(iterstep(:,1),iterstep(:,2));
    
44. %Draw the search trajectory

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[ 本帖最后由 suffer 于 2006-10-20 15:10 编辑 ]

suffer

gradobject1.m

1. %The following subfunction is on the gradient of
   
2. %the objective function
   
3. function y=gradobject1(v)
   
4. y(1)=2*v(1)-v(2)-10;
   
5. y(2)=2*v(2)-v(1)-4;

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suffer

goldsplictobj.m

1. %The following subfunction is on the goldspliction
   
2. %search of the substi function
   
3. function y=goldsplictobj(x)
   
4. a=0;
   
5. b=10;
   
6. eps=0.01;
   
7. y1=a+0.382*(b-a);
   
8. y2=a+0.618*(b-a);
   
9. while abs(b-a)>eps
   
10.    if substi(y1,x)>substi(y2,x)
    
11.       a=y1;
    
12.       b=b;
    
13.       y1=a+0.382*(b-a);
    
14.       y2=a+0.618*(b-a);
    
15.    elseif substi(y2,x)>substi(y1,x)
    
16.       a=a;
    
17.       b=y2;
    
18.       y1=a+0.382*(b-a);
    
19.       y2=a+0.618*(b-a);
    
20.    else
    
21.       a=y1;
    
22.       b=y2;
    
23.       y1=a+0.382*(b-a);
    
24.       y2=a+0.618*(b-a);
    
25.    end
    
26. end
    
27. y=(y1+y2)/2;

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suffer

object1.m

1. %The following subfunction is on the objective function
   
2. function y=object1(v)
   
3. y=v(1)^2+v(2)^2-v(1)*v(2)-10*v(1);

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suffer

substi.m

1. %The following subfunction is on the comming
   
2. %search function of alpha
   
3. function y=substi(alpha,x)
   
4. y=feval(@object1,x-alpha*gradobject1(x));

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lnljun

谢谢，初学最优化。

yisuibinlan

真的很谢谢楼主你！我想问下楼主拟牛顿法的程序，你懂吗？

ChaChing

新手无法看到登录资讯吗?
楼主是位高手, 但快一年没来了!

qqchun

非常感谢，