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A primal barrier function Phase I algorithm for nonsymmetric conic optimization problems
http://hdl.handle.net/2241/118163
http://hdl.handle.net/2241/1181632c09a941-5079-497f-8f1b-4a2c5aeb9eff
名前 / ファイル | ライセンス | アクション |
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JJIAM_29-3.pdf (229.5 kB)
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Item type | Journal Article(1) | |||||
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公開日 | 2013-01-25 | |||||
タイトル | ||||||
タイトル | A primal barrier function Phase I algorithm for nonsymmetric conic optimization problems | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
著者 |
Matsukawa, Yasuaki
× Matsukawa, Yasuaki× Yoshise, Akiko |
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著者別名 |
吉瀬, 章子
× 吉瀬, 章子 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | We call a positive semidefinite matrix whose elements are nonnegative a doubly nonnegative matrix, and the set of those matrices the doubly nonnegative cone (DNN cone). The DNN cone is not symmetric but can be represented as the projection of a symmetric cone embedded in a higher dimension. In Yoshise and Matsukawa (Proceedings of 2010 IEEE Multi-conference on Systems and Control, 2010), the authors demonstrated the efficiency of the DNN relaxation using the symmetric cone representation of the DNN cone. They showed that the DNN relaxation gives significantly tight bounds for a class of quadratic assignment problems, but the computational time is not affordable as long as we employ the symmetric cone representation. They then suggested a primal barrier function approach for solving the DNN optimization problem directly, instead of using the symmetric cone representation. However, most of existing studies on the primal barrier function approach have assumed the availability of a feasible interior point. This fact means that those studies are not inextricably tied to the practical usage. Motivated by these observations, we propose a primal barrier function Phase I algorithm for solving conic optimization problems over the closed convex cone K having the following properties: (a) its interior int K is not necessarily symmetric, (b) a self-concordant function f is defined over int K, and (c) its dual cone K* is not explicit or is intractable, all of which are observed when K is the DNN cone. We analyze the algorithm and provide a sufficient condition for finite termination. | |||||
書誌情報 |
Japan journal of industrial and applied mathematics 巻 29, 号 3, p. 499-517, 発行日 2012-10 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0916-7005 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA10799861 | |||||
DOI | ||||||
識別子タイプ | DOI | |||||
関連識別子 | 10.1007/s13160-012-0081-1 | |||||
権利 | ||||||
権利情報 | ©The JJIAM Publishing Committee and Springer 2012. The original publication is available at www.springerlink.com | |||||
著者版フラグ | ||||||
値 | author | |||||
出版者 | ||||||
出版者 | Springer | |||||
URI | ||||||
識別子 | http://hdl.handle.net/2241/118163 | |||||
識別子タイプ | HDL |