Right! A couple more interesting (IMO) example of this:

1. The geometric mean is the minimizer of:

L(x) = Σ [ log(x_i) - log(x) ]²

2. The so-called Jaccard median is the minimizer of:

L(x) = Σ [ 1-J(x_i, x) ]

where J is the Jaccard overlap score (aka, IoU = Intersection over Union). The second is interesting because the Jaccard score is often used to describe how close two segmentations are in image processing. The Jaccard median can be used to consolidate multiple segmentations of the same object in such a way that is best under the Jaccard distance.