AMPL Gurobi Define Variables Bounds

Question

I am trying to define both upper and lower bounds for a vector of variables in AMPL (solver Gurobi). However, after solving to optimal solution, the variables violate the bounds. The only way these bounds work is defined as explicit constraint in AMPL through the 'subject to' clause. Any idea why AMPL doesn't accept the bounds defined in the first way?

The first way:

var pi{t in 1..T} >= lb_pi[t] <= ub_pi[t];

The explicit way:

subject to C_pi_low{t in 1..T}:
    pi[t] >= lb_pi[t];

subject to C_pi_up{t in 1..T}:
    pi[t] <= ub_pi[t];

Answer 1

I am going to answer my own question. After I made the post, I realized the variable pi actually don't show up in the model though declared. It looks like this is the reason why the first way doesn't take effective in the 'solve' process while the second explicit way works.

Answer 2

According to section 14-1 of AMPL book:

For continuous variables, normally AMPL passes to solvers the first set of bounds, but you can instruct it to pass the second set by changing option var_bounds to 2 from its default value of 1. When active-set methods (like the simplex method) are applied, the second set tends to give rise to more degenerate variables, and hence more degenerate iterations that may impede progress toward a solution.

Reference: https://ampl.com/BOOK/CHAPTERS/17-solvers.pdf