There has been significant interest in distributed optimization algorithms, motivated by applications in Big Data analytics, smart grid, vehicle networks, etc. While there have been extensive theory and theoretical advances, a proportionally small body of scientific literature focuses on numerical evaluation of the proposed methods in actual practical, parallel programming environments. This paper considers a general algorithmic framework of first and second order methods with sparsified communications and computations across worker nodes. The considered framework subsumes several existing methods. In addition, a novel method that utilizes unidirectional sparsified communications is introduced and theoretical convergence analysis is also provided. Namely, we prove R-linear convergence in the expected norm. A thorough empirical evaluation of the methods using Message Passing Interface (MPI) on a High Performance Computing (HPC) cluster is carried out and several useful insights and guidelines on the performance of algorithms and inherent communication-computational trade-offs in a realistic setting are derived.
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