3 papers
math.OC2024
The structure of Gram matrices of sum of squares polynomials with restricted harmonic support
Mitchell Tong Harris
Some sum of squares (SOS) polynomials admit decomposition certificates, or positive semidefinite Gram matrices, with additional structure. In this work, we use the structure of Gra…
cs.LG2023
Learning Polynomial Problems with Equivariance
Hannah Lawrence, Mitchell Tong Harris
Optimizing and certifying the positivity of polynomials are fundamental primitives across mathematics and engineering applications, from dynamical systems to operations research. H…
math.OC2023
Improved Nonnegativity Testing in the Bernstein Basis via Geometric Means
Mitchell Tong Harris, Pablo A. Parrilo
We develop a new kind of nonnegativity certificate for univariate polynomials on an interval. In many applications, nonnegative Bernstein coefficients are often used as a simple wa…