How to change a function from Min(F(x)) to -Max(-F(x))?

Question

I have not a good knowledge in math field, I am working on multi objective functions, and I have two maximization functions, and one minimize function, where:

• Max (X,Y) = X+Y
• Max (L,M) = Sum (LC + MD), where C and D are constants.
• Min (T)= T*C.

I want to turn the two Max functions to Minimize function, how the function will be ?

Answer 1

In order to maximize X+Y, you can minimize -(X+Y), and then negate the optimal objective value. The optimal X and Y will also be optimal for maximize X+Y.

Similarly, to maximize Sum (LC + MD), you can minimize -Sum (LC + MD), and then negate the optimal objective value.