# An example from Luenberger 
# (Intro to  Linear and Nonlinear Prog. (1984), the chain problem)
# written in AMPL by Yu-Ju Kuo and Hans D. Mittelmann, 6/2001
param N;
param NH;
param NG;
param N2:=N/2;
var X{i in 1..N}:=if(N2+1<=i<=N) then sqrt(1-(16/N)^2) else -sqrt(1-(16/N)^2);
minimize obj:sum{i in 1..N}(N-i+.5)*X[i];
s.t. hx1:-16+sum{j in 1..N}sqrt(1-X[j]^2)=0;
s.t. hx2: sum{j in 1..N}X[j]=0;
s.t. g1i{i in 1..N}: X[i]+1>=0; 
s.t. g2i{i in N+1..NG}: 1-X[i-N]>=0;  

data;
param N:=50;
param NH:=2;
param NG:=100;