Primal-dual optimization methods for large-scale and distributed data analytics

12/18/2019
by   Dusan Jakovetic, et al.
0

The augmented Lagrangian method (ALM) is a classical optimization tool that solves a given "difficult" (constrained) problem via finding solutions of a sequence of "easier"(often unconstrained) sub-problems with respect to the original (primal) variable, wherein constraints satisfaction is controlled via the so-called dual variables. ALM is highly flexible with respect to how primal sub-problems can be solved, giving rise to a plethora of different primal-dual methods. The powerful ALM mechanism has recently proved to be very successful in various large scale and distributed applications. In addition, several significant advances have appeared, primarily on precise complexity results with respect to computational and communication costs in the presence of inexact updates and design and analysis of novel optimal methods for distributed consensus optimization. We provide a tutorial-style introduction to ALM and its analysis via control-theoretic tools, survey recent results, and provide novel insights in the context of two emerging applications: federated learning and distributed energy trading.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset