On Decentralized Tracking with ADMM for Problems with Time-Varying Curvature

Abstract

We analyze the performance of the alternating direction method of multipliers (ADMM) to track, in a decentralized manner, a solution of a stochastic sequence of optimization problems parametrized by a discrete time Markov process. The main advantage of considering a stochastic model is that we allow the objective functions to occasionally lose strong convexity and/or Lipschitz continuity of their gradients. Due to the stochastic nature of our model, the tracking statement is given in a mean square deviation error.