Control of distributed convex optimization

This paper addresses the problem of solving unconstrained, separable, convex optimization problems over networks and introduces a new approach to the problem: control of distributed convex optimization. We first develop Hopwise Equalizing (HE), a non-gradient-based, distributed asynchronous iterative algorithm that is asymptotically convergent and that is capable of solving the problem. Based on the framework provided by HE, we then develop Controlled Hopwise Equalizing (CHE), showing that a common Lyapunov function, constructed based on the first-order convexity condition, can be used to incorporate the notion of greedy, decentralized, feedback iteration control, whereby individual nodes use potential drops in the value of the Lyapunov function to control, on their own, when to initiate an iteration. Finally, via extensive simulation on wirelessly connected random geometric graphs, we show that CHE is significantly more bandwidth/energy efficient than several existing subgradient algorithms, requiring far less communications to solve a convex optimization problem.