Fair end-to-end window-based congestion control
IEEE/ACM Transactions on Networking (TON)
Krasovskii's method in the stability of network control
ACC'09 Proceedings of the 2009 conference on American Control Conference
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
The Impact of Stochastic Noisy Feedback on Distributed Network Utility Maximization
IEEE Transactions on Information Theory
A tutorial on cross-layer optimization in wireless networks
IEEE Journal on Selected Areas in Communications
Distributed convergence to Nash equilibria in two-network zero-sum games
Automatica (Journal of IFAC)
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This paper considers dynamic laws that seek a saddle point of a function of two vector variables, by moving each in the direction of the corresponding partial gradient. This method has old roots in the classical work of Arrow, Hurwicz and Uzawa on convex optimization, and has seen renewed interest with its recent application to resource allocation in communication networks. This paper brings other tools to bear on this problem, in particular Krasovskii's method to find Lyapunov functions, and recently obtained extensions of the LaSalle invariance principle for hybrid systems. These methods are used to obtain stability proofs of these primal-dual laws in different scenarios, and applications to cross-layer network optimization are exhibited.