6 papers
Toward a Systematic Understanding and Interactive Search of Lyapunov-Style Proofs in Optimization
TaeHo Yoon, Jaewook J. Suh, Edward Duc Hien Nguyen +2
Lyapunov-style convergence proofs, which establish a nonincreasing sequence to provide a quantitative convergence rate for an algorithm, are popular and often considered desirable…
Exact worst-case convergence rates for Douglas--Rachford and Davis--Yin splitting methods
Edward Duc Hien Nguyen, Jaewook J. Suh, Xin Jiang +1
In this work, we aim to establish the exact worst-case convergence rates of Douglas--Rachford splitting (DRS) and Davis--Yin splitting (DYS) when applied to convex optimization pro…
Sparse factorization of the square all-ones matrix of arbitrary order
Xin Jiang, Edward Duc Hien Nguyen, César A. Uribe +1
In this paper, we study sparse factorization of the (scaled) square all-ones matrix of arbitrary order. We introduce the concept of hierarchically banded matrices and propose t…
On graphs with finite-time consensus and their use in gradient tracking
Edward Duc Hien Nguyen, Xin Jiang, Bicheng Ying +1
This paper studies sequences of graphs satisfying the finite-time consensus property (i.e., iterating through such a finite sequence is equivalent to performing global or exact ave…
On the Performance of Gradient Tracking with Local Updates
Edward Duc Hien Nguyen, Sulaiman A. Alghunaim, Kun Yuan +1
We study the decentralized optimization problem where a network of agents seeks to minimize the average of a set of heterogeneous non-convex cost functions distributedly. State…
On Acceleration of Gradient-Based Empirical Risk Minimization using Local Polynomial Regression
Ekaterina Trimbach, Edward Duc Hien Nguyen, César A. Uribe
We study the acceleration of the Local Polynomial Interpolation-based Gradient Descent method (LPI-GD) recently proposed for the approximate solution of empirical risk minimization…