Krasovskii´s method in the stability of network control

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.