Constraint Feasibility Checks & Actions

[pedromxavier]

When generating penalty functions for constraints like $$a x + b \le 0$$ i.e. $$g(x) \le 0$$ one might go for $$\rho_k (g_k(x) + s)^{2} = 0, g(x) \in \text{PBF}$$ to compose the objective function.

As it is expected from PBF's that go $$ g: \mathbb{B}^{n} \to [a, b] $$, we can compute $$ [l, u] $$ such that $$ [a, b] \subseteq [l, u] $$ which gives us checks on wheter the function is infeasible or even always feasible. Tests against MOI's Knapsack were successful in detecting this case.

The question is: what to do when such things happen?

My first suggestion is:

# -*- Bounds & Slack Variable -*-
l, u = PBO.bounds(g)

s = if u < zero(T) # Always feasible
    @warn "Always-feasible constraint detected"
    continue
elseif l > zero(T) # Infeasible
    @warn "Infeasible constraint detected"
    error()
else
    VM.expansion(VM.encode!(VM.Binary, model, nothing, zero(T), abs(l)))
end

Although, I also suggest for continue and error() to be triggered by flags such as :ignore_feasible and :error_infeasible. Setting MOI termination status seems appropriate in the latter.