Optimization flow control—I: basic algorithm and convergence
IEEE/ACM Transactions on Networking (TON)
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
Utility-Optimal Random-Access Control
IEEE Transactions on Wireless Communications
Cross-Layer Congestion and Contention Control for Wireless Ad Hoc Networks
IEEE Transactions on Wireless Communications
A tutorial on cross-layer optimization in wireless networks
IEEE Journal on Selected Areas in Communications
Stability of primal-dual gradient dynamics and applications to network optimization
Automatica (Journal of IFAC)
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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.