Can an optimization problem be solved so that some finite number of randomly initialized points in $d$-dimensional Euclidean space (where $d \geq 2$) are positioned on a circle, sphere or hypersphere?
Points inside or outside the circle are "pushed" to the circle. Can this be done for a circle with predefined radius or any arbitrary circle? Here are some illustrations:
I can think of maximizing or minimizing the Euclidean distance of the points and a center within a constraint if $R$ is known, but what if this $R$ is not known or we do not have information about center or we don’t care?