Nearest points on toric varieties


  • Martin Helmer
  • Bernd Sturmfels



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.


Supplementary website,, copy at, code also at

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How to Cite

Helmer, M., & Sturmfels, B. (2018). Nearest points on toric varieties. MATHEMATICA SCANDINAVICA, 122(2), 213–238.