A Unified Approach to Analyzing Asynchronous Coordinate Descent and Tatonnement

This paper concerns asynchrony in iterative processes, focusing on gradient descent and tatonnement, a fundamental price dynamic. Gradient descent is an important class of iterative algorithms for minimizing convex functions. Classically, gradient descent has been a sequential and synchronous process, although distributed and asynchronous variants have been studied since the 1980s. Coordinate descent is a commonly studied version of gradient descent. In this paper, we focus on asynchronous coordinate descent on convex functions F : R → R of the form