Does Arthur Miller's claim that tragedy can be optimistic fit with Aristotle's theory of tragedy?
Miller's claim that tragedy *can* be optimistic (as stated in his essay "Modern Tragedy") is comparable to the Aristotelian notion of "catharsis". "Catharsis" is the final stage of a tragedy and means purgation: so that, after fear and pity have been aroused, the play releases those emotions and puts the turbulent events of its plot to rest (usually through death).
Catharsis is, if you like, the calm after the storm of a tragedy, and has been interpreted by some classical scholars as an optimism arising from the most profound despair - the hope of a new start.
But remember that no-one knows the precise status of the "Poetics" (the work that Aristotle's theory of tragedy is taken from) - it could be lecture notes taken by a student at Aristotle's lecture, it could be Aristotle's notes: we just don't know. And it is hugely ambiguous, not least because it is incomplete (we know that - at least - a section on comedy is missing). Aristotle isn't nearly as definite about tragedy as some people would have you believe!