Understanding Asynchronous Parallel Pattern Search

Asynchronous parallel pattern search (APPS) is a nonlinear optimization algorithm that dynamically initiates actions in response to events, rather than cycling through a fixed set of search directions, as is the case for synchronous pattern search. This gives us a versatile concurrent strategy that allows us to effectively balance the computational load across all available processors. However, the semi-autonomous nature of the search complicates the analysis. We concentrate on elucidating the concepts and notation required to track the iterates produced by APPS across all participating processes. To do so, we consider APPS and its synchronous counterpart (PPS) applied to a simple problem. This allows us both to introduce the bookkeeping we found necessary for the analysis and to highlight some of the fundamental differences between APPS and PPS.