Lyapunov Constructions for System Interconnections Arising from Adaptation in Some Optimization Methods
This work proves that interconnected systems from adaptive gradient methods are globally asymptotically stable (GAS). It provides three specific constructions of Lyapunov functions—V0, V1, and V2—that certify this stability. These functions are unique because they are built directly from the properties of the cost function and its derivatives rather than relying on generic subsystem dissipation rates.