102 citations · 200 across the 13 of their papers we have counts for
29 papers
An algebraic geometry approach to nonlinear parametric optimization in control
Ioannis A. Fotiou, Philipp Rostalski, Bernd Sturmfels +1
We present a method for nonlinear parametric optimization based on algebraic geometry. The problem to be studied, which arises in optimal control, is to minimize a polynomial funct…
Combinatorial secant varieties
Bernd Sturmfels, Seth Sullivant
The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant…
Matroid polytopes, nested sets and Bergman fans
Eva Maria Feichtner, Bernd Sturmfels
The tropical variety defined by linear equations with constant coefficients is the Bergman fan of the corresponding matroid. Building on a self-contained introduction to matroid po…
Tropical Mathematics
David Speyer, Bernd Sturmfels
These are the notes for the Clay Mathematics Institute Senior Scholar Lecture which was delivered by Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture…
Toric ideals of phylogenetic invariants
Bernd Sturmfels, Seth Sullivant
Statistical models of evolution are algebraic varieties in the space of joint probability distributions on the leaf colorations of a phylogenetic tree. The phylogenetic invariants…
On the rank of a tropical matrix
M. Develin, F. Santos, B. Sturmfels
This is a foundational paper in tropical linear algebra, which is linear algebra over the min-plus semiring. We introduce and compare three natural definitions of the rank of a mat…