# Estimating objective function weights from Pareto front

Let's say I have 2 functions $f_1(x)$ and $f_2(x)$. I ran a multi-objective optimization method to obtain the Pareto Front. Now, take any point P on the Pareto front. Assuming the Pareto Front to be convex, is there a way to back calculate the weights of the combined objective function,

$f(x) = \alpha f_1(x) + (1-\alpha) f_2(x)$

-