Â鶹ӰԺ

Distributed Convex and Nonconvex Optimization Over Time-varying Networks

In this talk, we discuss distributed optimization over time-varying networks. We revisit some of the recently
developed distributed optimization techniques including averaging-based methods, saddle-point-based
dynamics, and push-sum-based dynamics. We show that all of these dynamics are special cases of a broader
class of dynamics and control systems. We briefly sketch the proof of this result and discuss some of the
immediate implications of it. We then discuss a distributed optimization solver for a non-convex separable
optimization problem. We show that under some conditions the averaging-based distributed optimization
solver converges to a critical point of the objective function. Furthermore, we show that with the introduction
of a perturbation, each agent’s updates will converge (almost surely) to a local minima of the underlying
problem.