I have a sequence of convex sets $C_\lambda$ for $\lambda \in \mathbb{R}$ such that for $\lambda_1 > \lambda_2$, we have $C_{\lambda_1} \subset C_{\lambda_2}$ (essentially a nested sequence of convex sets in $d$ dimensions). For a given point $x \in \mathbb{R}^d$, define: \begin{align*}f(x) = \sup \{ \lambda: x \in C_{\lambda} \} \end{align*} Is there an efficient algorithm for computing $f(x)$ given $x$. 
Algorithm for testing if a point belongs to a sequence of convex set or not
ds.algorithms;convex geometry