Let $f(x,y)$ be a non-separable, non-negative real-valued function, that is jointly concave in $x$ and $y$. We want to maximize $f(x,y)$ over $x$ and $y$.
Is the sequential maximization $$\max_{x} \max_{y} f(x,y)$$ always equal to the simultaneous maximization $$\max_{x,\ y} f(x,y)$$ Or is there a simple counter-example for this?
I know that if $f(x,y)$ is separable, then the sequential maximization and simultaneous maximization are equal. Are there any conditions on a non-separable function such that this result still holds?
Any help is much appreciated!