Krasovskii's method in the stability of network control
Diego Feijer, Fernando Paganini · 2009
We consider network resource allocation problems based on convex optimization, and their decentralized solutions by means of primal, dual, or primal-dual subgradient control. We show how Krasovskii's method, that seeks Lyapunov functions which are quadratic forms of the vector field, provides new global stability proofs for various problems of this kind. Applications include congestion control, cross-layer congestion and contention control, and other general network utility maximization problems. We show more generally how this proof method applies to concave-convex saddle point problems solved by subgradient methods.