Geodesic
On an iterative method for solving linear programming problems on cluster computing systems
Numerical methods and programming, Tome 21 (2020) no. 3, pp. 329-340

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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.
Keywords: linear programming; large-scale problems; apex-method; predictor-corrector framework; iterative method; parallel algorithm; cluster computing system. 
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     author = {L. B. Sokolinskii and I. M. Sokolinskaya},
     title = {On an iterative method for solving linear programming problems on cluster computing systems},
     journal = {Numerical methods and programming},
     pages = {329--340},
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     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/VMP_2020_21_3_a10/}
}
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L. B. Sokolinskii; I. M. Sokolinskaya. On an iterative method for solving linear programming problems on cluster computing systems. Numerical methods and programming, Tome 21 (2020) no. 3, pp. 329-340. http://geodesic.mathdoc.fr/item/VMP_2020_21_3_a10/