On approximating D-induced polar sets of a second-order cone by an ellipsoid

doi:10.1080/09720502.2008.10700562

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	On approximating D-induced polar sets of a second-order cone by an ellipsoid
	Sun, Churen
刊名	JOURNAL OF INTERDISCIPLINARY MATHEMATICS
	2008
卷号	11 期号:3 页码:331-355
关键词	Robust optimization polyhedral approximation second-order cone
ISSN号	0972-0502
DOI	10.1080/09720502.2008.10700562
英文摘要	This article investigates approximatively describing the set F = { [A(0),..., A(n)] vertical bar A(0) + Sigma (n)(i = 1) s(i)A(i) epsilon kappa, for all s epsilon U } that kappa is a second-order cone while U is an ellipsoid. The concept of approximation degree is brought forward, and a box relaxation approximation method is proposed. For improving the approximation degree, the idea of approximating a second-order cone by a polyhedral cone is applied, and it's shown that approximating F by a tractable set with a preset approximation degree can be attained. Moreover, the dimension of such a tractable set grows polynomially with respect to the approximation degree. The results are extended to the case that kappa is a general p-th-order cone, while U is an ellipsoid, where p is rational or irrational.
WOS研究方向	Mathematics
语种	英语
出版者	TARU PUBLICATIONS
WOS记录号	WOS:000213667300002
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/2571]
专题	上海财经大学
通讯作者	Sun, Churen
作者单位	Shanghai Univ Finance & Econ, Inst Econ, Yangpu 200433, Peoples R China
推荐引用方式 GB/T 7714	Sun, Churen. On approximating D-induced polar sets of a second-order cone by an ellipsoid[J]. JOURNAL OF INTERDISCIPLINARY MATHEMATICS,2008,11(3):331-355.
APA	Sun, Churen.(2008).On approximating D-induced polar sets of a second-order cone by an ellipsoid.JOURNAL OF INTERDISCIPLINARY MATHEMATICS,11(3),331-355.
MLA	Sun, Churen."On approximating D-induced polar sets of a second-order cone by an ellipsoid".JOURNAL OF INTERDISCIPLINARY MATHEMATICS 11.3(2008):331-355.