This problem generalizes the spectral norm of a matrix (p = q = 2) and the Grothendieck problem (p = ∞, q = 1), and has been widely studied in various regimes. When p ≥ q, the problem exhibits a… (More)

We consider the (`p, `r)-Grothendieck problem, which seeks to maximize the bilinear form yT Ax for an input matrix A ∈ Rm×n over vectors x, y with ‖x‖p = ‖y‖r = 1. The problem is equivalent to… (More)

This problem generalizes the spectral norm of a matrix (p = q = 2) and the Grothendieck problem (p = ∞, q = 1), and has been widely studied in various regimes. When p ≥ q, the problem exhibits a… (More)

2017 IEEE 58th Annual Symposium on Foundations of…

2017

We consider the following basic problem: given an n-variate degree-d homogeneous polynomial f with real coefficients, compute a unit vector x in R{\string^}n that maximizes abs(f(x)). Besides its… (More)

We summarize the 1995 paper of Alon and Orlitsky, “Repeated Communication and Ramsey Graphs” [1], in which the authors characterize the capacity of channels with adversarial noise which is unbounded… (More)

We prove an analog of Parikh’s theorem for weighted context-free grammars over commutative, idempotent semirings, and exhibit a stochastic context-free grammar with behavior that cannot be realized… (More)

A number of recent works have studied algorithms for entrywise `p-low rank approximation, namely algorithms which given an n × d matrix A (with n ≥ d), output a rank-k matrix B minimizing ‖A − B‖p =… (More)