Non-convex distributed optimization

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

Our analysis shows that this perturbed procedure converges at a rate of O (1/t)

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

Distributednonconvexoptimization Distributed algorithms dealing with special instances of Problem (P) are scarce; they include primal methods [ 4, 12, 43, 45] and dual-based schemes [ 21, 54 ]

The key features of these algorithms are summarized in Table 1 and discussed next