Benchmarking Parallelization Models through Karmarkar's Interior-point method

Marco Edoardo Santimaria, Samuele Fonio, Giulio Malenza, Iacopo Colonnelli, Marco Aldinucci

Abstract: Optimization problems are one of the main focus of scientific research. Their computational-intensive nature makes them prone to be parallelized with consistent improvements in performance. This paper sheds light on different parallel models for accelerating Karmarkar's Interior-point method. To do so, we assess parallelization strategies for individual operations within Karmarkar's algorithm using OpenMP, GPU acceleration with CUDA, and the recent Parallel Standard C++ Linear Algebra library (PSTL) executing both GPU and CPU. Our different implementations yield interesting benchmark results that show the optimal approach for parallelizing interior point algorithms for general Linear Programming (LP) problems. In addition, we propose a more theoretical perspective of the parallelization of this algorithm, with a detailed study of our OpenMP implemen-tation, showing the limits of optimizing the single operations.