L-DATR: A Limited-Memory Distributed Asynchronous Trust-Region Method

A distributed approach is proposed in this work to solve large-scale optimization problems, called L-DATR, under the master/worker communication model. L-DATR is a distributed limited-memory trust-region method that allows worker nodes to perform asynchronous computations. Our method dynamically adjusts the step size and direction using trust-region strategies to improve stability and convergence. To our knowledge, this is the first implementation of a distributed trust-region limited memory quasi-Newton method with robust handling of asynchronous updates and non-uniform delays between nodes. Our method is communication-efficient because it communicates only vectors of the dimension of the decision variable. Our numerical experiments match our theoretical results and showcase significant stability improvements compared to state-of-the-art distributed algorithms.