I am wondering what the differences are between element-wise and jointly concave functions. How does an element-wise function look? I cannot imagine 2d function which is concave in terms of each variable but not concave jointly.
If we want to maximize a function with multiple variables, we should find the stationary point if the function is jointly concave. What should we do if the function is element-wise concave but not jointly concave? Under what conditions is the stationary point the optimal point if the function is element-wise concave?