半定规划的齐次内点算法的Matlab实现

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software Pub Date : 1999-01-01 DOI:10.1080/10556789908805763

Nathan W. Brixius, F. Potra, Rongqin Sheng

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引用次数: 34

摘要

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。

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

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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来源期刊

Optimization Methods & Software 工程技术-计算机：软件工程

CiteScore

4.50

自引率

0.00%

发文量

审稿时长

7 months

期刊介绍： Optimization Methods and Software publishes refereed papers on the latest developments in the theory and realization of optimization methods, with particular emphasis on the interface between software development and algorithm design. Topics include: Theory, implementation and performance evaluation of algorithms and computer codes for linear, nonlinear, discrete, stochastic optimization and optimal control. This includes in particular conic, semi-definite, mixed integer, network, non-smooth, multi-objective and global optimization by deterministic or nondeterministic algorithms. Algorithms and software for complementarity, variational inequalities and equilibrium problems, and also for solving inverse problems, systems of nonlinear equations and the numerical study of parameter dependent operators. Various aspects of efficient and user-friendly implementations: e.g. automatic differentiation, massively parallel optimization, distributed computing, on-line algorithms, error sensitivity and validity analysis, problem scaling, stopping criteria and symbolic numeric interfaces. Theoretical studies with clear potential for applications and successful applications of specially adapted optimization methods and software to fields like engineering, machine learning, data mining, economics, finance, biology, or medicine. These submissions should not consist solely of the straightforward use of standard optimization techniques.