3 citations · 3 across the 5 of their papers we have counts for
6 papers · 1 filter
Algebraic Distance Optimization in Polyhedral Norms
Eliana Duarte, Nidhi Kaihnsa, Julia Lindberg +2
We consider the distance minimization problem to a real algebraic variety $X \subseteq \RR^n$ when the metric is induced by a polyhedral norm. Each point in the variety has a Voron…
Efficient Tensor Decomposition via Moment Matrix Extension
Bobby Shi, Julia Lindberg, Joe Kileel
Motivated by a flurry of recent work on efficient tensor decomposition algorithms, we show that the celebrated moment matrix extension algorithm of Brachat, Comon, Mourrain, and Ts…
Symmetric Hyperbolic Polynomials
Grigoriy Blekherman, Julia Lindberg, Kevin Shu
Hyperbolic polynomials have been of recent interest due to applications in a wide variety of fields. We seek to better understand these polynomials in the case when they are symmet…
The algebraic degree of sparse polynomial optimization
Julia Lindberg, Leonid Monin, Kemal Rose
We study a broad class of polynomial optimization problems whose constraints and objective functions exhibit sparsity patterns. We give two characterizations of the number of criti…
Exploiting Symmetry in the Power Flow Equations Using Monodromy
Julia Lindberg, Nigel Boston, Bernard C. Lesieutre
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 su…
The Distribution of the Number of Real Solutions to the Power Flow Equations
Julia Lindberg, Alisha Zachariah, Nigel Boston +1
In this paper we study the distributions of the number of real solutions to the power flow equations over varying electrical parameters. We introduce a new monodromy and parameter…