Lyapunov analyses for first-order methods : Theory, automation, and algorithm design
This thesis, comprising four research papers, contributes to the field of systematic and computer-aided analyses and design of first-order methods. The first two papers focus on developing new methodologies, while the remaining two apply these techniques to refine complexity and convergence results, as well as to design new methods. A central theme of the work is the use of Lyapunov-type analyses,
