# Chain : a discretized version of the well known porblem of shortest chain 
# between two points under force gravity
# (nonconvex and badly conditioned)
# written in AMPL by Yu-Ju Kuo and Hans D. Mittelmann, 6/2001
param N:=50;
param NH:=1;
param NG:=0;
param KL:=4;
param YA:=1;
param YE:=3;
param DT:=1/(N+1);
var X{i in 1..N}:=YA+(YE-YA-KL)*2*DT*i+2*(2*KL-(YE-YA))*DT*i*(DT*i-.5);
param N1:=N+1;
param DTH:=.5*DT;
var YM{i in 1..N1}=if(i==1) then (X[i]+YA)*.5 else if (i==N1)then (YE+X[i-1])*.5 else(X[i]+X[i-1])*.5;
var YS{i in 1..N1}=if(i==1) then (X[i]-YA)/DT else if (i==N1)then (YE-X[i-1])/DT else (X[i]-X[i-1])/DT;
var W{i in 1.. N1}=sqrt(1+YS[i]^2);
minimize obj : DT*sum{i in 1..N1}YM[i]*W[i];
s.t.    hx : DT*sum{i in 1..N1}W[i]-KL=0;