Nearest Points on Toric Varieties

Abstract

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.

20 pages

References in corpus (1)

• Chern-Mather classes of toric varieties

Cited by in corpus (9)

• The Maximum Likelihood Degree of Toric Varieties
• Principal Landau Determinants
• Symbol Alphabets from the Landau Singular Locus
• The Distance Function from a Real Algebraic Variety
• Euclidean distance degree and limit points in a Morsification
• Local Euler obstructions of toric varieties
• Chern-Mather classes of toric varieties
• A Morse theoretic approach to non-isolated singularities and applications to optimization
• Higher order polar and reciprocal polar varieties