On the Convergence of Asynchronous Parallel Pattern Search

In this paper the authors prove global convergence for asynchronous parallel pattern search. In standard pattern search, decisions regarding the update of the iterate and the step-length control parameter are synchronized implicitly across all search directions. They lose this feature in asynchronous parallel pattern search since the search along each direction proceeds semi-autonomously. By bounding the value of the step-length control parameter after any step that produces decrease along a single search direction, they can prove that all the processes share a common accumulation point and that such a point is a stationary point of the standard nonlinear unconstrained optimization problem