function y = Min_F1(xk,z_k)
%MIN_F Summary of this function goes here
%  Detailed explanation goes here
a=0;
b=50;
l=0.00001;
x1=a+0.382*(b-a);
x2=a+b-x1;
while(abs(b-a)>l)
    x_temp1=xk+x1.*z_k;
     x_temp2=xk+x2.*z_k;
     if(F(x_temp1)>F(x_temp2))
        a=x1;
        if (abs(b-a)>l)  
          x1=x2;
         x2=a+0.618*(b-a);
        end 
     else
        b=x2;
        if (abs(b-a)>l) 
	      x2=x1;
	      x1=a+0.382*(b-a);
        end  
     end
end
y=(a+b)/2;