How to differentiate under summation


(Ramy Ramy) #1

Hi All,

I have a concave problem that I have checked concavity from simulation, and I wonder if someone is familiar with how to get the first derivative for the function encompassing summation.

Obj(alpha) = (alpha/k) \sum_{n=k+1}^{ceil( (k/2)*(1+1/alpha) )} log2(1 + fn(n))

fn(n) is a function of alpha since the summation bound has alpha. assume any concave function for fn(n), how to differentiate Obj(alpha) w.r.t. alpha
alpha is a scalar


(Mark L. Stone) #2

Why do you think that function is differentiable with respect to alpha? The occurrence of ceil, not to mention that the summation bound needs to be an integer (which ceil accomplishes) does not seem very differentiable to me.

If a function is not differentiable, concavity will need to be determined in some other way than by differentiation.