Generalized Continuous-Time Models for Nesterov's Accelerated Gradient Methods

ArXi:2409.00913v2 Announce Type: replace-cross Recent research has indicated a substantial rise in interest in understanding Nestero's accelerated gradient methods via their continuous-time models. However, most existing studies focus on specific classes of Nestero's methods, which hinders the attainment of an in-depth understanding and a unified perspective. To address this deficit, we present generalized continuous-time models that cover a broad range of Nestero's methods, including those previously studied under existing continuous-time frameworks. Our key contributions are as follows.