TITLE: Do computational geometers use Lagrange multipliers?
QUESTION [6 upvotes]: Can anyone point me to an example of a problem that (more or less) originated in computational geometry whose solution requires the use of Lagrange multipliers (or Kuhn-Tucker conditions, or dual variables in a linear program, etc.)?  I have not been able to find such an example in any of the literature that I own.

REPLY [3 votes]: A convex optimization method for constructing a set of points in the plane with prescribed (combinatorial) Delaunay triangulation is given in 
Euclidean structures on simplicial surfaces and hyperbolic volume
I Rivin - Annals of Mathematics, 1994