研究生《最优化方法》课程实验-最优化编程作业答案-东北大学

研究生《最优化方法》课程实验（第一部分）

function a=li_H(x1,x2,f1,f2)

t1=0.00001;t2=0.00001;t3=0.0001;

a=0;

if norm(grad(x2))>=t3

a=1;

end

if (norm(x2-x1))/(norm(x1)+1)>=t1

a=1;

end

if (abs(f2-f1))/(abs(f1)+1)>=t2

a=1;

end

end

---------------------------------------------------------------------------------------------------------------------- function t= line(f,a,b,e)

B=0.618;

t2=a+B *(b-a);

hanshu2=subs(f,t2);

t1=a+b-t2;

f1=subs(f,t1);

while abs(t1-t2)>=e

if f1<=f2

b=t2;

t2=t1;

f2=f1;

t1=a+b-t2;

f1=subs(f,t1);

else

a=t1;

t1=t2;

f1=f2;

t2=a+B *(b-a);

f2=subs(f,t2);

end

end

tb=0.5*(t1+t2);

fb=subs(f,tb);

f2=tb;

---------------------------------------------------------------------------------------------------------------------- function y=qujian(x,p)

t0=0.000001;h=0.5;

y0=fv(x+t0*p);t2=t0+h;y2=fv(x+t2*p);

if y2>=y0

t1=t2;y1=y2;h=-h;

t2=t0+h;y2=fv(x+t2*p);

while(y2<=y0)

t1=t0;y1=y0;t0=t2;y0=y2;h=2*h;

t2=t0+h;y2=fv(x+t2*p);

end

a=min(t1,t2);b=max(t1,t2);

else

t1=t0;y1=y0;t0=t2;y0=y2;h=2*h;t2=t0+h;y2=fv(x+t2*p);

while(y2<=y0)

t1=t0;y1=y0;t0=t2;y0=y2;h=2*h;

t2=t0+h;y2=fv(x+t2*p);

end

a=min(t1,t2);b=max(t1,t2);

end

sq=[a,b];

end

----------------------------------------------------------------------------------------------------------------------syms t

q=1;

f=input(' 请输入目标函数: ','s');

M=sym(input(' 请输入目标函数的变量: ','s'));

x0=input(' 请输入计算的初值: ');

f0=subs(f,M,x0);

g=jacobian(f,M);

g0=subs(g,M,x0);

p0=-g0;

H0=eye(length(M));

x1=x0-t*p0;

yt=subs(f,M,x1);

v=qujian (yt,0.001,0);

t0=line(yt,v(1),v(3),0.001);

x1=x0-t0*p0;

f1=subs(f,M,x1);

g1=subs(g,M,x1);

xk=x0;

xk1=x1;

Hk=H0;

gk=g0;

gk1=g1;

disp('中间运行结果')

disp('n=1')

disp('x=')

fprintf(1,'%7.5f\n',xk')

fprintf(1,'f(x)=%7.5f\n',f1)

n=1;

fk=f0;

fk1=f1;

flag= li_H(xk,xk1,fk,fk1);

while flag==0

n=n+1;

sk=xk1-xk;

yk=gk1-gk;

Hk1=Hk+(sk'*sk)/(sk*yk')-(Hk*yk'*yk*Hk)/(yk*Hk*yk');

pk1=Hk1*gk1';

xk=xk1;

xk1=xk-t*pk1';

yt=subs(f,M,xk1);

v=qujian(yt,0.001,0);

tk=line(yt,v(1),v(3),0.001);

xk1=xk-tk*pk1' ;

fk=subs(f,M,xk);

gk=subs(g,M,xk);

fk1=subs(f,M,xk1);

gk1=subs(g,M,xk1);

fprintf(1,'n=%7.5f\n',n)

disp('x=')

fprintf(1,'%7.5f\n',xk1)

fprintf(1,'f(x)=%7.5f\n',fk1)

flag= li_H(xk,xk1,fk,fk1);

if flag==0

disp('不是极小点需要继续迭代')

end

end

if q==1

disp(' 目标函数的最优解是:');

fprintf(1,' %7.5f\n',xk);

disp(' 迭代次数为n=')

fprintf(1,'%7.5f\n',n)

disp('最优解是:')

fprintf(1,'%7.5f\n',fk1)

end

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