オハラ　アツミ   Atsumi Ohara   小原　敦美    所属   追手門学院大学  理工学部 数理・データサイエンス学科    職種   教授
言語種別	英語
発行・発表の年月	2014/04
形態種別	外国学術誌（その他）
査読	査読あり
標題	Curvature integrals and iteration complexities in SDP and symmetric cone programs
執筆形態	共著・編著（代表編著を除く）
掲載誌名	COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
掲載区分	国外
出版社・発行元	SPRINGER
巻・号・頁	57(3),pp.623-665
著者・共著者	Satoshi Kakihara,Atsumi Ohara,Takashi Tsuchiya
概要	In this paper, we study iteration complexities of Mizuno-Todd-Ye predictor-corrector (MTY-PC) algorithms in SDP and symmetric cone programs by way of curvature integrals. The curvature integral is defined along the central path, reflecting the geometric structure of the central path. Integrating curvature along the central path, we obtain a precise estimate of the number of iterations to solve the problem. It has been shown for LP that the number of iterations is asymptotically precisely estimated with the integral divided by , where beta is the opening parameter of the neighborhood of the central path in MTY-PC algorithms. Through numerical experiments with large SDP instances from SDPLIB, we demonstrate that the number of iterations is explained quite well with the integral even for a large step size which is enough to solve practical large problems.
DOI	10.1007/s10589-013-9608-x
ISSN	0926-6003/1573-2894