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Gossip Algorithms for Convex Consensus Optimization Over Networks
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DOI：10.1109/TAC.2011.2160020.png)
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In many applications, nodes in a network desire not only a consensus, but an optimal one. To date, a family of subgradient algorithms have been proposed to solve this problem under general convexity assumptions. This technical note shows that, for the scalar case and by assuming a bit more, novel non-gradient-based algorithms with appealing features can be constructed. Specifically, we develop Pairwise Equalizing (PE) and Pairwise Bisectioning (PB), two gossip algorithms that solve unconstrained, separable, convex consensus optimization problems over undirected networks with time-varying topologies, where each local function is strictly convex, continuously differentiable, and has a minimizer. We show that PE and PB are easy to implement, bypass limitations of the subgradient algorithms, and produce switched, nonlinear, networked dynamical systems that admit a common Lyapunov function and asymptotically converge. Moreover, PE generalizes the well-known Pairwise Averaging and Randomized Gossip Algorithm, while PB relaxes a requirement of PE, allowing nodes to never share their local functions.
Keyword:
Distributed consensus
distributed convex optimization
gossip algorithms
networked dynamical systems
期刊
IF:
7
论文数:
1.3W
被引数:
6.7W
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Consensus and cooperation in networked multi-agent systems网络化多智能体系统的共识与合作.png)
PROCEEDINGS OF THE IEEE
PROCEEDINGS OF THE IEEEIF25.9
PREAI
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