Nearest Points on Toric Varieties
  We determine the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the $A$-discriminant in terms of Euler obstructions. Our primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point. 
Martin Helmer and Bernd Sturmfels
math.AG cs.SC math.OC