Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 56, Issue 12, Pages 2911-2918Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2011.2160020
Keywords
Distributed consensus; distributed convex optimization; gossip algorithms; networked dynamical systems
Funding
- National Science Foundation [CMMI-0900806, EEC-0755011]
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [0900806] Funding Source: National Science Foundation
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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.
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