Hans Mittleman test various optimization software packages on his benchmark website. One of the test problems is ns1687037. An inspection of that problem reveals many constraint blocks of the form
R0002624: 5.015e+004 C0024008 ....+ C0025749 = 5.0307748e+007
R0002625: 0e+000 <= - C0025749 + C0025750
R0002626: 0e+000 <= C0025749 + C0025750
R0002627: 1.9877659e-008 C0025750 - C0025751 = 0e+000
C0025749 is free
These constraints implies
-C0025750 <= C0025749 <= C0025750
1.9877659e-008 C0025750 = C0025751
and hence
1.9877659e-008 abs( C0025749) <= C0025751
In other words variable C0025749 is an elastic/penalty variable for constraint R0002624. Moreover, we see variable C0025751 is identical 1.0e-8 of the elastic variable in constraint R0002624. Now the right hand side of constraint R0002624 is 10^7 and hence it is more or less the rounding error that is penalized. That makes me wonder if that model provides reliable results or does what the author wants!
