A predictor-corrector algorithm for linear optimization based on a specific self-regular proximity function

doi:10.1137/040603991

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	A predictor-corrector algorithm for linear optimization based on a specific self-regular proximity function
	Peng, JM ; Terlaky, T ; Zhao, YB
	2005
发表期刊	SIAM JOURNAL ON OPTIMIZATION
ISSN	1052-6234
卷号	15 期号:4 页码:1105-1127
摘要	It is well known that the so-called first-order predictor-corrector methods working in a large neighborhood of the central path are among the most efficient interior-point methods (IPMs) for linear optimization (LO) problems. However, the best known iteration complexity of this type of method is O(n log (x(0))(T)s(0)/epsilon). It is of interest to investigate whether the complexity of first-order predictor-corrector type methods can be further improved. In this paper, based on a specific self-regular proximity function, we de. ne a new large neighborhood of the central path. In particular, we show that the new neighborhood matches the standard large neighborhood that is defined by the infinity norm and widely used in the IPM literature. A new first-order predictor-corrector method for LO that uses a search direction induced by self-regularity in corrector steps is proposed. We prove that our predictor-corrector algorithm, working in a large neighborhood, has an O(root n log n log (x(0))(T)s(0)/epsilon) iteration bound. Local superlinear convergence of the algorithm is also established.
关键词	linear optimization interior-point methods predictor-corrector self-regular proximity function large neighborhoods polynomial complexity superlinear convergence
DOI	10.1137/040603991
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000231357600009
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2004
专题	中国科学院数学与系统科学研究院
通讯作者	Peng, JM
作者单位	1.McMaster Univ, Dept Comp & Software, Hamilton, ON L8S 4L7, Canada 2.Chinese Acad Sci, AMSS, Inst Appl Math, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Peng, JM,Terlaky, T,Zhao, YB. A predictor-corrector algorithm for linear optimization based on a specific self-regular proximity function[J]. SIAM JOURNAL ON OPTIMIZATION,2005,15(4):1105-1127.
APA	Peng, JM,Terlaky, T,&Zhao, YB.(2005).A predictor-corrector algorithm for linear optimization based on a specific self-regular proximity function.SIAM JOURNAL ON OPTIMIZATION,15(4),1105-1127.
MLA	Peng, JM,et al."A predictor-corrector algorithm for linear optimization based on a specific self-regular proximity function".SIAM JOURNAL ON OPTIMIZATION 15.4(2005):1105-1127.