I have a maximization problem with an objective function of two variables. To prove the concavity of the function, is it sufficient to prove that it is concave with respect to each of the variables? Does the concavity of the function wrt each variable result in its joint concavity?
Thank you in advance.
No, Take $f(x,y)=xy$, this function is concave (even Linear!) with respect to each argument, but not Jointly concave. Look at its Hessian !