Maximize::vdom
Minimize::vdom
Reduce`Infimum::vdom
Reduce`Supremum::vdom
An error occurs because Primes is not a supported domain in Minimize:
Minimize[{2x y + 5 y ^ 2 + 2x ^ 2 + 7y - x + 5, Element[{x, y}, Primes]}, {x, y}]This shows a valid use of Minimize with domain Integers:
Minimize[{2x y + 5 y ^ 2 + 2x ^ 2 + 7y - x + 5, Element[{x, y}, Integers]}, {x, y}]