Numerical Maximization with Alternating Sum

Question

I need to maximize a function that involves an alternating sum and a set of constraints. I have tried the following code:

NMaximize[{(-1)^{m}*n!, n + m == 7, m > 0, n > 0}, {m, n}]

However, the error message

NMaximize: The objective function {(-1)^m n!} should be scalar-valued

appears.

Are there any numerical maximization methods that can be used for functions like this?

Answer 1

(1) Change (-1)^{m} to (-1)^(m) and (2) add the constraint that m and n are integers:

NMaximize[{(-1)^(m)*n!, n + m == 7, m > 0, n > 0, Element[{m, n}, Integers]}, {m, n}]

{6., {m -> 4, n -> 3}}