On Parallel or Distributed Asynchronous Iterations with Unbounded Delays and Possible Out of Order Messages or Flexible Communication for Convex Optimization Problems and Machine Learning

We describe several features of parallel or distributed asynchronous iterative algorithms such as unbounded delays, possible out of order messages or flexible communication. We concentrate on the concept of macro-iteration sequence which was introduced in order to study the convergence or termination of asynchronous iterations. A survey of asynchronous iterations for convex optimization problems is also presented. Finally, a new result of convergence for parallel or distributed asynchronous iterative algorithms with flexible communication for convex optimization problems and machine learning is proposed.