Sdpha: a Matlab implementation of homogeneous interior-point algorithms for semidefinite programming

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 1999-01-01 DOI:10.1080/10556789908805763

Nathan W. Brixius, F. Potra, Rongqin Sheng

引用次数: 34

Abstract

Mehrotra type primal-dual predictor-corrector interior-point algorithms for semidefinite programming are implemented, using the homogeneous formulation proposed and analyzed by Potra and Sheng. Several search directions, including the AHO, HKM, NT, Toh, and Gu directions, are used. A rank-2 update technique is employed in our MATLAB code so that the computation of homogeneous directions is only slightly more expensive than in the non-homogeneous case. However, the homogeneous algorithms generally take fewer iterations to compute an approximate solution within a desired accuracy. Numerical results show that the homogeneous algorithms outperform their non-homogeneous counterparts, with improvement of more than 20% in many cases, in terms of total CPU time.

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半定规划的齐次内点算法的Matlab实现

利用Potra和Sheng提出并分析的齐次公式，实现了半定规划的Mehrotra型原对偶预测校正内点算法。使用了几个搜索方向，包括who、HKM、NT、Toh和Gu方向。在我们的MATLAB代码中采用了rank-2更新技术，因此齐次方向的计算只比非齐次情况下的计算稍微昂贵。然而，齐次算法通常需要较少的迭代才能在期望的精度范围内计算近似解。数值结果表明，就总CPU时间而言，齐次算法优于非齐次算法，在许多情况下提高了20%以上。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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