Monotone Inclusion

Monotone inclusion problems, focusing on finding solutions where the sum of multiple operators equals zero, are central to many optimization and equilibrium problems across diverse fields. Current research emphasizes efficient algorithms like Halpern iteration and its variants (e.g., inexact and variance-reduced versions), often applied within neural network architectures to solve these problems, particularly in machine learning contexts such as robust optimization and game theory. These advancements improve convergence rates and computational efficiency, impacting applications ranging from image processing and distributionally robust optimization to formal verification of neural network controlled systems. The development of robust and efficient solvers for monotone inclusions continues to be a significant area of investigation, driven by the increasing prevalence of these problems in modern applications.