Monotone Operator

Monotone operators, mathematical objects with a specific non-decreasing property, are central to solving a wide range of problems in areas like image processing and machine learning. Current research focuses on developing efficient algorithms, such as the Forward-Backward-Forward and Chambolle-Pock algorithms, to leverage monotone operators within neural networks for tasks like inverse problems and density estimation. This involves exploring both the theoretical convergence properties of these algorithms, particularly under conditions of non-monotonicity or local monotonicity, and their practical application in improving the performance and robustness of deep learning models, especially in high-dimensional settings. The resulting advancements offer improved solutions for challenging inverse problems and enhanced capabilities in probabilistic modeling.