MATLAB实现最速下降法

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1、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-Fistheobjectfunctioninputasstring'F'%      -G=(-1/norm)(gradF)*gradF;thesearchdirection%      inputasastring'G'%      -P0istheinitialstratingpoint  %  

2、    -maxlisthemaximumnumberofinteractions%      -deltaisthetoleranceforthehmininthesingle%      parameterminuizationinthesearchdirection%      -epsilonisthetolerancefortheerroriny0%      -show;ifshow==1theiterationsaredisplay%Output-P0isthepointofminium%      -y0isthefunctionvalueF(P0)%      -

3、erriserrorboundfory0%      -Pisavectorcontainingtheiterationsifnargin==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(len>1e4),h=len/le4;enderr=1;cnt=0;cond=0;P(cnt+1,:)=[P0y0];while(cnt<maxl&cond~=5&(h>delta

4、

5、err<epsilon))    %Computesearchdirection    S=feval(G,P0);    %Startsingleparameterquadraticminimization    P1=P0+h*S;    P2=P0+2*h*S;    y1=feval(F,P1);    y2=feval(F,P2);    cond=0;j=0;    while(j<maxj&cond==0)        len=norm(P0);        if(y0<y1)            P2

6、=P1;            y2=y1;            h=h/2;            P1=P0+h*S;            y1=feval(F,P1);        else            if(y2<y1)                P1=P2;                y1=y2;                h=2*h;                P2=P0+2*h*S;                y2=feval(F,P2);            else                cond=-1;

7、            end        end        j=j+1;        if(h<delta),cond=1;end        if(abs(h)>big

8、len>big),cond=5;end    end        if(cond==5)        Pmin=P1;        ymin=y1;    else        d=4*y1-2*y0-2*y2;