  In this paper, the problem of computing the projection, and therefore the
minimum distance, from a point onto a Minkowski sum of general convex sets is
studied. Our approach is based on the minimum norm duality theorem originally
stated by Nirenberg and the Nesterov smoothing techniques. It is shown that
projection points onto a Minkowski sum of sets can be represented as the sum of
points on constituent sets so that, at these points, all of the sets share the
same normal vector which is the negative of the dual solution. The proposed
NESMINO algorithm improves the theoretical bound on number of iterations from
$O(\frac{1}{\epsilon})$ by Gilbert [SIAM J. Contr., vol. 4, pp. 61--80, 1966]
to $O\left(\frac{1}{\sqrt{\epsilon}}\ln(\frac{1}{\epsilon})\right)$, where
$\epsilon$ is the desired accuracy for the objective function. Moreover, the
algorithm also provides points on each component sets such that their sum is
equal to the projection point.
