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Non-Convex Distributed Optimization
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DOI：10.1109/TAC.2017.2648041.png)
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We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. The perturbed push-sum algorithm was previously used for convex distributed optimization. We generalize the result obtained for the convex case to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function, if the objective function has no saddle points. Our analysis shows that this perturbed procedure converges at a rate of O(1/t).
Keyword:
Non-convex optimization
time-varying multi-agent
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期刊
IF:
7
论文数:
1.3W
被引数:
6.7W
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