A high-performance software package for semidefinite programs: SDPA 7
A high-performance software package for semidefinite programs: SDPA 7
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发表时间：
2010
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通讯作者：
M. Yamashita;K. Fujisawa;K. Nakata;Maho Nakata;Mituhiro Fukuda;Kazuhiro Kobayashi;Kazushige Goto
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作者：
M. Yamashita;K. Fujisawa;K. Nakata;Maho Nakata;Mituhiro Fukuda;Kazuhiro Kobayashi;Kazushige Goto
众所周知，1995年启动的SDPA（半决赛编程算法）项目可提供用于解决大规模半决赛计划（SDP）的高性能包装。 SDPA VER。 6求解了大规模密集的SDP，但是，与其他软件包相比，它需要大量的计算时间，尤其是当Schur补体矩阵稀疏时。 SDPA VER。 7现在已从SDPA VER完全修订。 6特别是在以下三个实施中； （i）修改变量的存储和内存访问来处理由大量亚介导组成的变量矩阵，（ii）具有稀疏Schur补体矩阵的SDP的快速稀疏Cholesky分解，（iii）在A上并行实现具有复杂技术的多核处理器可减少线程冲突。结果，SDPA VER。 7可以求解由较短时间且内存少的各个字段产生的SDP。 6和其他软件包。此外，借助多个精度库，基于SDPA实现SDPA-GMP，-QD和-DD，以非常准确稳定的计算执行原始的偶内点方法。本文的目的是介绍SDPA VER的简短解释。 7并通过数值实验报告其对大规模密集和稀疏的地位的高性能，与一般SDP的其他一些主要软件包相比。数值实验还显示了SDPA -GMP，-QD和-DD的惊人数值准确性。
The SDPA (SemiDefinite Programming Algorithm) Project launched in 1995 has been known to provide high-performance packages for solving large-scale Semidefinite Programs (SDPs). SDPA Ver. 6 solves eciently large-scale dense SDPs, however, it required much computation time compared with other software packages, especially when the Schur complement matrix is sparse. SDPA Ver. 7 is now completely revised from SDPA Ver. 6 specially in the following three implementation; (i) modification of the storage of variables and memory access to handle variable matrices composed of a large number of sub-matrices, (ii) fast sparse Cholesky factorization for SDPs having a sparse Schur complement matrix, and (iii) parallel implementation on a multi-core processor with sophisticated techniques to reduce thread conflicts. As a consequence, SDPA Ver. 7 can eciently solve SDPs arising from various fields with shorter time and less memory than Ver. 6 and other software packages. In addition, with the help of multiple precision libraries, SDPA-GMP, -QD and -DD are implemented based on SDPA to execute the primal-dual interior-point method with very accurate and stable computations. The objective of this paper is to present brief explanations of SDPA Ver. 7 and to report its high performance for large-scale dense and sparse SDPs through numerical experiments compared with some other major software packages for general SDPs. Numerical experiments also show the astonishing numerical accuracy of SDPA-GMP, -QD and -DD.