conjugate_gradient.m

压缩包里包含了无约束优化问题常用的几种求解方法的源程序：变量轮换法（variable_rotation.m）、最速下降法（steepest_descent.m）、修正牛顿法（modified_newt

function [min,solvec,stepnum]=conjugate_gradient(str,ini,err)
%  File name:conjugate_gradient.m      
%  Author:Yan Anxin
%  ID number:081810
%  Date:finished on 2008.11.15
%  Description:  
%       Here defines a function,to solve the bivariate unconstrained optimization problems by conjugate-gradient-method
%       In the syntax [min,solvec,stepnum]=conjugate_gradient(str,ini,err),
%       str----input,means the expression of objective function
%       ini----input,sets the starting point to ini 
%       err----input,sets admissible error
%       min=conjugate_gradient(str,ini,err) attempts to find min, i.e. the minimum of objective function   
%       [min,solvec]=conjugate_gradient(str,ini,err) returns solvec, i.e. the minimum point  
%       [min,solvec,stepnum]=conjugate_gradient(str,ini,err) returns stepnum,i.e. the times of iterative 
           
[A,b]=coefficient_matrix(str);      %calls the function coefficient_matrix(str) to obtain the coefficient
A=A.*2;
x(:,1)=ini;
n=2;k=2;stepnum=0;
sol=[inf,inf]';
while k==n
    L(:,1)=A*x(:,1)+b;
    if norm(L(:,1))<=err,sol=x(:,1);break,end
    p(:,1)=-(A*x(:,1)+b);k=1;
    while k~=n
        gamma(:,k)=-(A*x(:,k)+b)'*p(:,k)/((p(:,k))'*A*p(:,k));
        x(:,k+1)=x(:,k)+gamma(:,k)*p(:,k);
        if norm(A*x(:,k+1)+b)<=err,sol=x(:,k);break,end
        beta(:,k)=-(A*x(:,k+1)+b)'*p(:,k)/((p(:,k))'*A*p(:,k));
        p(:,k+1)=-(A*x(:,k)+b);         %gets the direction of search
        k=k+1;stepnum=stepnum+1;        
    end    
    if sol==x(:,k),break,end
    x(:,1)=x(:,n);
end

solvec=sol;
min=minval(str,solvec);                %calls the function minval(str,solvec) to obtain the minimum value