Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to
study polynomial equations. Its origins were methods to solve systems of polynomial …

We present numerical homotopy continuation algorithms for solving systems of equations on
a variety in the presence of a finite Khovanskii basis. These homotopies take advantage of …

Améndola et al. proposed a method for solving systems of polynomial equations lying in a
family which exploits a recursive decomposition into smaller systems. A family of systems …

In this paper we study the distributions of the number of real solutions to the power flow
equations over varying electrical parameters. We develop a new monodromy and parameter …

The method of moments is a statistical technique for density estimation that solves a system
of moment equations to estimate the parameters of an unknown distribution. A fundamental …

As Jordan observed in 1870, just as univariate polynomials have Galois groups, so do
problems in enumerative geometry. Despite this pedigree, the study of Galois groups in …

We propose solving the power flow equations using monodromy. We prove the variety under
consideration decomposes into trivial and nontrivial subvarieties and that the nontrivial …

This work utilizes toric varieties for solving systems of equations. In particular, it includes two
numerical homotopy continuation algorithms for numerically solving systems of equations …

Operation and planning of electric grids involve the analysis of certain power flow equations,
which exhibit multiple solutions. One solution generally corresponds to a preferred operating …

In this paper we study the Shor relaxation of quadratic programs by fixing a feasible set and
considering the space of objective functions for which the Shor relaxation is exact. We first …