运筹学实验共轭梯度法.docx

文档介绍：共轭梯度法
一、实验目的
(1).熟悉使用共轭梯度法求解无约束非线性规划问题的原理；
(2).在掌握原理的基础上熟练运用此方法解决问题；
(3).学会利用计算机语言编写程序来辅助解决数学问题；
(4).解决问题的同时分析问题，力求=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)