On an iterative method for solving linear programming problems on cluster computing systems: The paper was recommended by the Programm Committee of th International Conference "Russian Supercomputing Days" - Sokolinsky, L.B.; Sokolinskaya, Irina (Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie), 2020)
The paper is devoted to a new method for solving large-scale linear programming (LP) problems. This method is called the apex-method. The apex-method uses the predictor–corrector framework. Thepredictor step calculates a point belonging to the feasible region of the LP problem. The corrector step calculates a sequence of points converging to the exact solution of the LP problem. The paper gives a formal description of the apex-method and provides information about its parallel implementation in C++ language using the MPI library. The results of large-scale computational experiments on a cluster computing system to study the scalability of the apex method are discussed.