How to define the step size of steepest-descent method and update the step size simultaneously in multiple variable function?

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Jinghua Li 2016-11-24

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https://ww2.mathworks.cn/matlabcentral/answers/313751-how-to-define-the-step-size-of-steepest-descent-method-and-update-the-step-size-simultaneously-in-mu

How to define the step size of steepest descent method and update the step size simultaneously in multiple variable function? As following, the initial value of 2-dimensional object function are x0 and y0, but if i view { (x1’,y1’), (x2’,y2’) … (xn’,yn’) } as the initial value and i view f=[(x1-2)^2+(y1-4)^2]*[(x2-2)^2+(y2-4)^2]…[(xn-2)^2+(yn-4)^2] as the object function.how to apply steepest-descent method to f? (For (x1,y1) lamda1 is its step size,for (x2,y2) lamda1 is its step size,… for (xn,yn) lamda1 is its step size.)

      % function [ R,n ] = steel(x0,y0,eps )
syms x;
syms y;
f=(x-2)^2+(y-4)^2;
v=[x,y];
j=jacobian(f,v);%计算梯度
T=[subs(j(1),x,x0),subs(j(2),y,y0)];
temp=sqrt((T(1))^2+(T(2))^2);
x1=x0;
y1=y0;
n=0;
syms kk;
while(temp>eps)
     d=T;%计算下降方向
     f1=x1+kk*d(1);
     f2=y1+kk*d(2);
     fT=[subs(j(1),x,f1),subs(j(2),y,f2)];
     fun=sqrt((T(1))^2+(T(2))^2);
     fun1=vpa(fun);
     x0=x1-0.1*d(1);
     y0=y1-0.1*d(2);
     T=[subs(j(1),x,x0),subs(j(2),y,y0)];
     temp=sqrt((T(1))^2+(T(2))^2);
     temp1=vpa(temp);
     x1=x0;
     y1=y0;
     n=n+1;
end
R=double([x0,y0]);