6 citations · 15 across the 16 of their papers we have counts for
16 papers
Bounds on the Semidefinite Programming Complexity of the Euclidean Ball
Guanxi Li, Kevin Shu
We present tight lower bounds for the size of any linear matrix inequality representation of the Euclidean ball, and on the semidefinite extension complexity of the ball. Specifica…
Lagrangian Dual Sections: A Topological Perspective on Hidden Convexity
Venkat Chandrasekaran, Timothy Duff, Jose Israel Rodriguez +1
Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optim…
Debiasing Polynomial and Fourier Regression
Chris Camaño, Raphael A. Meyer, Kevin Shu
We study the problem of approximating an unknown function by a degree- polynomial using as few function evaluations as possible, where error is measu…
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…
Hidden convexity, optimization, and algorithms on rotation matrices
Akshay Ramachandran, Kevin Shu, Alex L. Wang
This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices . Such problems are nonconvex due t…
Quadratic Programming with Sparsity Constraints via Polynomial Roots
Kevin Shu
Quadratically constrained quadratic programs (QCQPs) are an expressive family of optimization problems that occur naturally in many applications. It is often of interest to seek ou…
Linear Principal Minor Polynomials: Hyperbolic Determinantal Inequalities and Spectral Containment
Grigoriy Blekherman, Mario Kummer, Raman Sanyal +2
A linear principal minor polynomial or lpm polynomial is a linear combination of principal minors of a symmetric matrix. By restricting to the diagonal, lpm polynomials are in bije…
On the computational equivalence of co-NP refutations of a matrix being a P-matrix
Spencer Gordon, Kevin Shu
A P-matrix is a square matrix such that all principal submatrices of have positive determinant. Such matrices appear naturally in instances of the linear complementarity pr…
Approximate PSD-Completion for Generalized Chordal Graphs
Kevin Shu
Recently, there has been interest in the question of whether a partial matrix in which many of the fully defined principal submatrices are PSD is approximately PSD completable. The…
Extreme Nonnegative Quadratics over Stanley Reisner Varieties
Kevin Shu
We consider the convex geometry of the cone of nonnegative quadratics over Stanley-Reisner varieties. Stanley-Reisner varieties (which are unions of coordinate planes) are amongst…
Causal Channels
Kevin Shu
We consider causal models with two observed variables and one latent variables, each variable being discrete, with the goal of characterizing the possible distributions on outcomes…
Hyperbolic Relaxation of -Locally Positive Semidefinite Matrices
Grigoriy Blekherman, Santanu S. Dey, Kevin Shu +1
A successful computational approach for solving large-scale positive semidefinite (PSD) programs is to enforce PSD-ness on only a collection of submatrices. For our study, we let $…
Sums of Squares and Sparse Semidefinite Programming
Grigoriy Blekherman, Kevin Shu
We consider two seemingly unrelated questions: the relationship between nonnegative polynomials and sums of squares on real varieties, and sparse semidefinite programming. This con…
Phylogenetics of Indo-European Language families via an Algebro-Geometric Analysis of their Syntactic Structures
Kevin Shu, Andrew Ortegaray, Robert Berwick +1
Using Phylogenetic Algebraic Geometry, we analyze computationally the phylogenetic tree of subfamilies of the Indo-European language family, using data of syntactic structures. The…
Syntactic Structures and Code Parameters
Kevin Shu, Matilde Marcolli
We assign binary and ternary error-correcting codes to the data of syntactic structures of world languages and we study the distribution of code points in the space of code paramet…
Syntactic Phylogenetic Trees
Kevin Shu, Sharjeel Aziz, Vy-Luan Huynh +2
In this paper we identify several serious problems that arise in the use of syntactic data from the SSWL database for the purpose of computational phylogenetic reconstruction. We s…