13 papers · 1 filter
A Stochastic Alternating Direction Method of Multipliers for Non-smooth and Non-convex Optimization
Fengmiao Bian, Jingwei Liang, Xiaoqun Zhang
Alternating direction method of multipliers (ADMM) is a popular first-order method owing to its simplicity and efficiency. However, similar to other proximal splitting methods, the…
The Fun is Finite: Douglas-Rachford and Sudoku Puzzle -- Finite Termination and Local Linear Convergence
Robert Tovey, Jingwei Liang
In recent years, the Douglas-Rachford splitting method has been shown to be effective at solving many non-convex optimization problems. In this paper we present a local convergence…
Geometry of First-Order Methods and Adaptive Acceleration
Clarice Poon, Jingwei Liang
First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science…
SPRING: A fast stochastic proximal alternating method for non-smooth non-convex optimization
Derek Driggs, Junqi Tang, Jingwei Liang +2
We introduce SPRING, a novel stochastic proximal alternating linearized minimization algorithm for solving a class of non-smooth and non-convex optimization problems. Large-scale i…
Trajectory of Alternating Direction Method of Multipliers and Adaptive Acceleration
Clarice Poon, Jingwei Liang
The alternating direction method of multipliers (ADMM) is one of the most widely used first-order optimisation methods in the literature owing to its simplicity, flexibility and ef…
On Biased Stochastic Gradient Estimation
Derek Driggs, Jingwei Liang, Carola-Bibiane Schönlieb
We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is…