Why does GAMS return "infeasible" solution when I add lower bound?

GAMS
1

I have an objective function with a division involving a variable x.

  1. If I solve it, it returns error due to division by zero.

  2. If I add a lower bound, it halts and says infeasible solution.

Why would it do this? If I remove the term that involves division by zero, the problem becomes feasible (with a non-zero x), so clearly infeasibility is not the problem?

I managed to multiply through by x and get rid of the division, but is that really the only way? (It’s not possible every time either …)

2

In the NLP context, the “path” that the solver follows is non-trivial and faced with many challenges. All that you are observing is “normal” behaviour for this type of problems.

For the specific case of division, your approach:

I managed to multiply through by x and get rid of the division, but is that really the only way? (It’s not possible every time either …)

Is the usual advised approach. When would it be not possible ?

Best
Claudio