Given a continuous map $g:[0,1]\longrightarrow \mathbb{R}^{n}$, Somebody know an efficient algorithm to compute the (say, the Euclidean) distance from a point $P\in\mathbb{R}^{n}$ to $g(I)$?
Of course, it is an optimization problem of the form
$$ \min\{d(P,g(t)):t \in [0,1] \},$$
and as I need to solve the above problem for a set (large) of points $P$, such algorithm has to be as efficient as possible.
Thanks you in advance for your comments.