% ECE 111 Lecture 10
% Hanging Chain of length 10
% Calling routine
% y = -[1:9]'/9;
% cost_chain(y)
%[y,e] = fminsearch('cost_chain', y)

function [ J ] = cost_chain( Z )
 
   Y = [0;Z;0];
   PE = sum(Y);
   L = 0;
   for i=2:11
      L = L + sqrt(1 + (Y(i) - Y(i-1))^2);
   end
   
   E = (12 - L);
   J = PE + 100*E^2;
      
   plot([0:10],Y,'.-');
   ylim([-5,1]);
   pause(0.01);
      
   end