MATLAB实现最速下降法.doc

MATLAB实现最速下降法这个程序是一本美国的数值方法教材上提供的，程序清单如下：function p0,y0,err,P=grads(F,G,P0,maxl,delta,epsilon,show)%input -F is the object function input as string F%-G=(-1/norm)(grad F)*grad F;the search direction % input as a string G%-P0 is the initial strating point%-maxl is the maximum number of interactions%-delta is the tolerance for the hmin in the single % parameter minuization in the search direction %-epsilon is the tolerance for the error in y0%-show;if show=1 the iterations are display %Output-P0 is the point of minium %-y0 is the function value F(P0)%-err is error bound for y0%-P is a vector containing the iterationsif nargin=5,show=0;end m,n=size(P0);maxj=10;big=1e8;h=1;P=zeros(maxj,n+1);len=norm(P0);y0=feval(F,P0);if(len1e4),h=len/le4;enderr=1;cnt=0;cond=0;P(cnt+1,:)=P0 y0;while(cntdelta|errepsilon)%Compute search direction S=feval(G,P0);%Start single parameter quadratic minimizationP1=P0+h*S;P2=P0+2*h*S;y1=feval(F,P1);y2=feval(F,P2);cond=0;j=0;while(jmaxj&cond=0)len=norm(P0);if(y0y1)P2=P1;y2=y1;h=h/2;P1=P0+h*S;y1=feval(F,P1);elseif(y2y1)P1=P2;y1=y2;h=2*h;P2=P0+2*h*S;y2=feval(F,P2);elsecond=-1;endendj=j+1;if(hbig|lenbig),cond=5;endendif(cond=5)Pmin=P1;ymin=y1;elsed=4*y1-2*y0-2*y2;if(d0)hmin=h*(4*y1-2*y0-2*y2)/d;elsecond=4;hmin=h/3;end%constrcuct the next pointPmin=P0+hmin*S;ymin=feval(F,Pmin);%Determine magitude of next hh0=abs(hmin);h1=abs(hmin-h);h2=abs(hmin-2*h);if(h0h),h=h0;endif(h1h),h=h1;endif(h2h),h=h2;endif(h=0),h=hmin;endif(hdelta),cond=1;end%Terination test for minization e0=abs(y0-ymin);e1=abs(y1-ymin);e2=abs(y2-ymin);if(e0=0&e0err),err=e0;endif(e1=0&e1err),err=e1;endif(e2=0&e2err),err=e2;endif(e0=0&e1=0&e2=0),err=0;endif(errepsilon),cond=2;endif(cond=2&hde