Convex Analysis

Convex analysis provides a powerful mathematical framework for studying optimization problems, focusing on the properties of convex functions and sets to guarantee the existence and uniqueness of optimal solutions. Current research emphasizes applications in machine learning, including the development of stable and efficient neural network architectures like deep equilibrium models and the design of algorithms for safe and robust optimization under uncertainty, often leveraging techniques from mirror descent and proximal methods. These advancements are driving progress in areas such as hyperparameter tuning, adversarial robustness, and solving challenging problems in optimal transport and stochastic optimization, ultimately improving the performance and reliability of machine learning models.