Semismooth Newton

Semismooth Newton methods are iterative algorithms used to solve challenging optimization problems, particularly those involving non-smooth or nonsmooth functions, arising frequently in machine learning and statistics. Current research focuses on applying and improving these methods within various contexts, including optimal transport, graphical model estimation, and solving large-scale Lasso problems, often incorporating techniques like augmented Lagrangian methods and exploiting sparsity structures for computational efficiency. These advancements lead to faster and more scalable solutions for a wide range of applications, improving the feasibility and accuracy of complex data analysis tasks.