I have a "mathematical programming" (MP) problem that does not have an objective function. Namely, I want to find a vector that satisfies all constraints (no optimization involved, right?). Now, a couple of (maybe) silly questions come to my head:
A "mathematical programming" problem with no objective function is a valid mathematical programming problem?
Whatever the nature of this problem, it can be implemented in optimization software by adding a dummy objective function that is just ignored. So, is this an optimization problem or not? Is it an existence problem that may be solved by construction (finding the solution if it exists)?
Does this kind of problem have a particular name?