Transform a set of points to have a minimum distance between them Assume I have a set of $N$ ordered points, $X$. I would like to find the set of $N$ points, $Y$, where the distance between $X$ and $Y$ $(d = \sum_{i=0}^{N-1} |X_i - Y_i| )$ is minimized but there is a minimum distance between points of $M$ $(Y_{i+1} - Y_i &gt; M)$. Is there an algorithm or approach to deriving $Y$ given $X$ and $M$?
Using log-barrier constraints (suggestion from the comments) along with a Nelder-Mead simplex approach got fantastic results.
As clarification to some of the other comments, the points were in Euclidean space comprised of real numbers.