Abstract
A wider selection of step sizes is explored for the distributed subgradient algorithm for multigent optimization problems with time-varying and balanced communication topologies. The square summable requirement of the step sizes commonly adopted in the literature is removed. The step sizes are only required to be positive, vanishing, and nonsummable, which provides the possibility for better convergence rates. Both unconstrained and constrained optimization problems are considered. It is proved that the agents' estimates reach a consensus and converge to the minimizer of the global objective function with the more general choice of step sizes. The best convergence rate is shown to be the reciprocal of the square root of iterations for the best record of the function value at the average of the agents' estimates for the unconstrained case with the wider selection of step sizes. A simulation example is provided to show the effectiveness of the results.
| Original language | English |
|---|---|
| Pages (from-to) | 2295-2302 |
| Number of pages | 8 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 63 |
| Issue number | 7 |
| Early online date | 16 Oct 2017 |
| DOIs | |
| Publication status | Published - Jul 2018 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 1963-2012 IEEE.
Funding
This work was supported in part by the National Science Foundation under Grant ECCS–1611423, in part by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China under Grant 61321003, in part by the 111 Project (B17048), in part by the National Natural Science Foundation of China under Grant 61528301, Grant 61573082, and Grant 61203080, and in part by the Technology Transformation Program of Chongqing Higher Education University under Grant KJZH17102.
Keywords
- Cooperative control
- distributed optimization
- step sizes
- switching topologies