I need to solve an optimization problem. Please offer your insights.

Suppose there are two functions (my case is more complicated than this example).

f(x,y)=x-y, 0<x<1, 0<y<1

g(x,y)=x*y, 0<x<1, 0<y<1

The goal is to get the maximum values for f(x,y) and g(x,y). However, it is not simultaneous, but sequential. In the first stage, only x can be chosen to maximize f(x,y); in the second stage only y can be chosen to maximize g(x,y...