Scalable Parallel Algorithm for Solving Non-stationary Systems of Linear Inequalities

作     者：Sokolinsky, L. B. Sokolinskaya, I. M. 

作者机构：Natl Res Univ South Ural State Univ Chelyabinsk 454080 Russia 

出 版 物：《LOBACHEVSKII JOURNAL OF MATHEMATICS》 (罗巴切夫斯基数学杂)

年 卷 期：2020年第41卷第8期

页      面：1571-1580页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Russian Foundation for Basic Research [2007-00092-a] Ministry of Science and Higher Education of the Russian Federation [FENU-2020-0022] Government of the Russian Federation [A03.21.0011] 

主　　题：non-stationary system of linear inequalities feasibility problem iterative method parallel algorithm approximate solution cluster computing system 

摘      要：In this paper, a scalable iterative projection-type algorithm for solving non-stationary systems of linear inequalities is considered. A non-stationary system is understood as a large-scale system of inequalities in which coefficients and constant terms can change during the calculation process. The proposed parallel algorithm uses the concept of pseudo-projection which generalizes the notion of orthogonal projection. The parallel pseudo-projection algorithm is implemented using the parallel BSF-skeleton. An analytical estimation of the algorithm scalability boundary is obtained on the base of the BSF cost metric. The large-scale computational experiments were performed on a cluster computing system. The obtained results confirm the efficiency of the proposed approach.