5 papers
Accelerated Implicit GDA Schemes: Theoretical Guarantees and Application to Proximal Augmented Lagrangian Methods
Jiaqi Liu, Bin Shi
Convex optimization problems with linear equality constraints arise ubiquitously in scientific computing, machine learning, and control theory. Classical Krylov methods are effecti…
Numerical Solution for Nonlinear 4D Variational Data Assimilation (4D-Var) via ADMM
Bowen Li, Bin Shi
The four-dimensional variational data assimilation (4D-Var) has emerged as an important methodology, widely used in numerical weather prediction, oceanographic modeling, and climat…
A Lyapunov Analysis of Accelerated PDHG Algorithms
Xueying Zeng, Bin Shi
The generalized Lasso is a remarkably versatile and extensively utilized model across a broad spectrum of domains, including statistics, machine learning, and image science. Among…
Understanding the PDHG Algorithm via High-Resolution Differential Equations
Bowen Li, Bin Shi
The least absolute shrinkage and selection operator (Lasso) is widely recognized across various fields of mathematics and engineering. Its variant, the generalized Lasso, finds ext…
Understanding the ADMM Algorithm via High-Resolution Differential Equations
Bowen Li, Bin Shi
In the fields of statistics, machine learning, image science, and related areas, there is an increasing demand for decentralized collection or storage of large-scale datasets, as w…