I attended the 55th annual Allerton Conference on Communication, Control, and Computing in Monticello, IL. On the right is a photo of the view from the conference venue. You wouldn’t guess that this is in Illinois! At the conference, I presented an invited paper by my student Akhil Sundararajan and myself entitled “Robust convergence analysis of distributed optimization algorithms”. The paper describes a methodology based on semidefinite programming that allows one to efficiently analyze a variety of recently proposed distributed optimization algorithms (in the sense of bounding the worst-case convergence rate). The benefit of our method lies in its versatility. Convergence analyses typically require customized approaches for each algorithm, whereas our method is flexible and can be broadly and automatically applied. We present two methods: one for obtaining graph-dependent performance bounds and one for obtaining robust bounds that hold over the set of graphs with a given spectral gap. Slides from my talk are available here.