102 citations · 104 across the 4 of their papers we have counts for
4 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…
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…