Maximize::mixdom
Minimize::mixdom
Reduce`Infimum::mixdom
Reduce`Supremum::mixdom
An error occurs because the domain specification is only given for one of the variables:
Minimize[{2x ^ 2 + 2x y + 7y + y ^ 2 + 25, Element[x, Integers]}, {x, y}]This shows a valid use of Minimize with both variables restricted to domain Integers:
Minimize[{2x ^ 2 + 2x y + 7y + y ^ 2 + 25, Element[{x, y}, Integers]}, {x, y}]