Stability of primal-dual gradient dynamics and applications to network optimization

By Diego Feijer, Fernando Paganini. at - Automatisierungstechnik, 2010

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Design and Stability of Load-Side Primary Frequency Control in Power Systems (2013, neutral): “These results are proved in Section IV.”
A control perspective for centralized and distributed convex optimization (2011, methodology): “For a proof requiring twice differentiable cost and using a different Lyapunov function see [7].”
Linear convergence of primal-dual gradient methods and their performance in distributed optimization (2019, background): “Algorithms of the form (3) have been applied in various applications including but not limited to wireless systems [2], [3], power systems [4], reinforcement learning [5], and network utility maximization [6], [7].”
A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems (2017, methodology): “First proposed in [131] with more recent treatments in [132] and [133], the Gradient Dynamics (GD) technique embeds the KKT conditions for an optimization problem in a dynamical system.”
Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems (2015, methodology): “The following assumptions are given for (8), which were also adopted for the distributed optimization or resource allocation in Feijer & Paganini (2010), Kia, Cort´es, & Martinez (2015), and Liu & Wang (2015).”