共轭梯度法 MATLAB程序.doc

%conjugate gradient methods%method:FR,PRP,HS,DY,CD,WYL,LS%精确线搜索,梯度终止准则function m,k,d,a,X,g1,fv = conjgradme( G,b,c,X,e,method)if nargin=e k(i-1)=(m/m1)2; d(:,i)=-g1(:,i)+k(i-1)*d(:,i-1); a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i); %a1(i)=-(X(:,i)*G*d(:,i)+b*d(:,i)/(d(:,i)*G*d(:,i);a(i)=g1(:,i)*g1(:,i)/(d(:,i)*G*d(:,i); X(:,i+1)=X(:,i)+a(i)*d(:,i); g1=g1 subs(subs(g,x1,X(1,i+1),x2,X(2,i+1); m1=m; m=norm(g1(:,i+1); i=i+1; end case PRP while m=e k(i-1)=g1(:,i)*(g1(:,i)-g1(:,i-1)/(norm(g1(:,i-1)2; d(:,i)=-g1(:,i)+k(i-1)*d(:,i-1); a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i); X(:,i+1)=X(:,i)+a(i)*d(:,i); g1=g1 subs(subs(g,x1,X(1,i+1),x2,X(2,i+1); m=norm(g1(:,i+1); i=i+1; end case HS while m=e k(i-1)=g1(:,i)*(g1(:,i)-g1(:,i-1)/(d(:,i-1)*(g1(:,i)-g1(:,i-1); d(:,i)=-g1(:,i)+k(i-1)*d(:,i-1); a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i); X(:,i+1)=X(:,i)+a(i)*d(:,i); g1=g1 subs(subs(g,x1,X(1,i+1),x2,X(2,i+1); m=norm(g1(:,i+1); i=i+1; end case DY while m=e k(i-1)=g1(:,i)*g1(:,i)/(d(:,i-1)*(g1(:,i)-g1(:,i-1); d(:,i)=-g1(:,i)+k(i-1)*d(:,i-1); a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i); X(:,i+1)=X(:,i)+a(i)*d(:,i); g1=g1 subs(subs(g,x1,X(1,i+1),x2,X(2,i+1); m=norm(g1(:,i+1); i=i+1; end case LS while m=e k(i-1)=g1(:,i)*(g1(:,i)-g1(:,i-1)/(d(:,i-1)*(-g1(:,i-1); d(:,i)=-g1(:,i)+k(i-1)*d(:,i-1); a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i); %a(i)=-(X(:,i)*G*d(:,i)+b*d(:,i)/(d(:,i)*G*d(:,i); X(:,i+1)=X(:,i)+a(i)*d(:,i); g1=g1 subs(subs(g,x1,X(1,i+1),x2,X(2,i+1); m=norm(g1(:,i+1); i=i+1; end case CD while m=e k(i-1)=g1(:,i)*g1(:,i)/(d(:,i-1)*(-g1(:,i-1); d(:,i)=-g1(:,i)+k(i-1)*d(:,i-1); a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i); X(:,i+1)=X(:,i)+a(i)*d(:,i); g1=g1 subs(subs(g,x1,X(1,i+1),x2,X(2,i+1); m=norm(g1(:,i+1); i=i+1; end case WYL while m=e k(i-1)=g1(:,i)*(g1(:,i)-(m/m1)*g1(:,i-1)/(m12); d(:,i)=-g1(:,i)+k(i-1)*d(:,i-1); a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i); %a(i)=-(X(:,i)*G*d(:,i)+b*d(:,i)/(d(:,i)*G*d(:,i); X(:,i+1)=X(:,i)+a(i)*d(:,i); g1=g1 subs(subs(g,x1,X(1,i+1),x2,X(2,i+1); m1=m; m=norm(g1(:,i+1); i=i+1; endendfv=subs(subs(f,x1,X(1,i),x2,X(2,i); endl1=X(1,i);l2=X(2,i);w1=X(1,1);w2=X(2,1);v1=min(l1,w1)-abs(l1-w1)/10:abs(l1-w1)/10:max(l1,w1)+abs(l1-w1)/10;v2=min(l2,w2)-abs(l2-w2)/10:abs(l2-w2)/10:max(l2,w2)+abs(l2-w2)/10;x,y=meshgrid(v1,v2);s=size(x);z=zeros(size(x);for i=1:s(1) for j=1:s(2) z(i,j)=1/2*x(i,j),y(i,j)*G*x(i,j);y(i,j)+b*x(i,j);y(i,j)+c; endendpx,py = gradient(z,.2,.2);contour(v1,v2,z), hold o