How Stopping checks for optimality

The solver can let Stopping handles the optimality checks. We see here how it works and how to tune it in.

First, the function stop! computes a score using optimality_check function given in the meta. The keywords argument given in stop! are passed to this function.

#Compute the score if !src.optimality_check
score = stp.meta.optimality_check(stp.pb, stp.current_state; kwargs...))

The score is then stored in stp.current_state.current_score. If the score doesn't contain any NaN, Stopping proceeds and test whether it is within tolerances given as functions in meta.tol_check and meta.tol_check_neg.

#Compute the tolerances
check_pos, check_neg = tol_check(stp.meta)
#Test the score vs the tolerances
optimal = _inequality_check(optimality, check_pos, check_neg)

So, overall Stopping does:

check_pos = stp.meta.tol_check(stp.meta.atol, stp.meta.rtol, stp.meta.optimality0)
check_neg = stp.meta.tol_check_neg(stp.meta.atol, stp.meta.rtol, stp.meta.optimality0)
score     = stp.meta.optimality_check(stp.pb, stp.current_state)
check_pos ≤ score ≤ check_neg

FAQ: Does it work for vector scores as well?

The type of the score and tolerances are respectively initialized in the State and the Meta at the initialization of the Stopping. Hence one can use vectorized scores as long as they can be compared with the tolerances. For instance:

• The score is a vector and tolerances are vectors of the same length or numbers.
• The score is a tuple and tolerances are tuple or a number.

FAQ: How do I implement AND and OR conditions?

The concatenation of two scores (AND condition) that need to be tested to zero can be represented as a vector. The disjunction of two score (OR condition) are represented as tuple.

FAQ: Do Stopping really computes the tolerances each time?

It does unless meta.recomp_tol is set as true. This entry can be set as true from the beginning as the tol_check functions are evaluated once at the initialization of the meta.