6 papers
Local Linear Convergence of the Primal-Dual Hybrid Gradient Method for Semidefinite Programming
Xin Jiang
Primal-dual first-order methods are widely used for large-scale semidefinite programming (SDP), but their ability to compute highly accurate solutions is not well explained by glob…
A Relaxation and Rectification (ReCR) Framework for Systems with Linear and Complementary Constraints: Theoretical Foundation, Algorithms and Numerical Experiments
Wissam AlAli, Xin Jiang, Jiming Peng
Systems defined by linear and complementarity constraints (SLCCs) arise frequently in engineering, economics, and other related fields. They also appear in the optimality condition…
Local Linear Convergence of the Alternating Direction Method of Multipliers for Semidefinite Programming under Strict Complementarity
Shucheng Kang, Xin Jiang, Heng Yang
We investigate the local linear convergence properties of the Alternating Direction Method of Multipliers (ADMM) when applied to Semidefinite Programming (SDP). A longstanding beli…
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…
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…
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…