计算机科学 ›› 2011, Vol. 38 ›› Issue (9): 204-207.
• 人工智能 • 上一篇 下一篇
杨林峰,李陶深,李捷,陈燕
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YANG lin-feng,LI Tao-sheng, LI Jie, CHEN Yan
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摘要: 基于内点算法((Interior Point Method,IPM)框架,导出具有分块带边结构系数矩阵的线性规划(Linear Programming, I_P)问题的简化和最简修正方程,并证明最简修正方程的对角分块具有正定性。结合正定矩阵的Cholcsky分解和解藕技术设计了修正方程的并行求解方法,给出了LP的并行内点算法结构。集群环境下的数值实验表明,所提算法具有很好的加速比和可扩展性,适合求解大规模结构化工尹问题。
关键词: 线性规划,分块带边矩阵,并行算法,解藕,最简修正方程
Abstract: This paper presented the simpler and simplest correction equation of linear programming(LP) with block bordered coefficient matrix based on the framework of interior point method(IPM). And the diagonal sulrmatrix in the simplest correction equation was proved to be symmetric positive definite. Parallel IPM algorithm for LP was presented after a parallel solver for correction equation was proposed by integrating decoupling and Cholesky factorization of symmetric positive definite matrix The simulations in the cluster show that the proposed method is very promising for large scale LP problems due to its excellent speed up and scalability.
Key words: Linear programming, Block bordered matrix, Parallel algorithm, Decoupling, Simplest correction equation
杨林峰,李陶深,李捷,陈燕. 分块带边结构线性规划并行算法[J]. 计算机科学, 2011, 38(9): 204-207. https://doi.org/
YANG lin-feng,LI Tao-sheng, LI Jie, CHEN Yan. Parallel Algorithm of Block Bordered Linear Programming[J]. Computer Science, 2011, 38(9): 204-207. https://doi.org/
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