Maximum of weighted sum of exponentials

Question

Given a function $$f(t) := \sum_k a_k e^{b_k t} $$ for some $b_k < 0$, we want to find maximum of $f(t)$ over $t > 0$ algorithmically.

A solution would be to calculate $f'(t)$ and and then convert $e^{-t}$ to a new variable, say $z$, and find roots of a polynomial with (potentially) non-integer exponents. Is there any better algorithm in terms of computational complexity?

Answer 1

Newton’s algorithm is the way to go.