In recent decades, we have witnessed significant progresses in the convergence and complexity theory of the first-order optimization methods, with gradient global Lipschitz continuity (GGLC) assumption playing a central role, in many classical results. However, a large class of important problems arising in modern optimization and machine learning do not satisfy this assumption. As a result, there remains a substantial gap between the theory and practical behavior of many widely used algorithms.

This project, led by Dr. Zhang, aims to strengthen the theoretical foundation of relative smooth optimization, an emerging framework developed to go beyond the classical GGLC setting. In particular, the project will study first-order methods under relative smoothness, with a focus on nonconvex problems, more appropriate optimality measures, and new non-Euclidean Lipschitz tools that better capture the underlying problem geometry. The goal is to establish sharp...