{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T21:50:17Z","timestamp":1725745817940},"publisher-location":"Berlin, Heidelberg","reference-count":14,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642400193"},{"type":"electronic","value":"9783642400209"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-40020-9_87","type":"book-chapter","created":{"date-parts":[[2013,8,19]],"date-time":"2013-08-19T01:32:37Z","timestamp":1376875957000},"page":"777-784","source":"Crossref","is-referenced-by-count":0,"title":["Information Geometry and Interior-Point Algorithms"],"prefix":"10.1007","author":[{"given":"Satoshi","family":"Kakihara","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Atsumi","family":"Ohara","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takashi","family":"Tsuchiya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"87_CR1","unstructured":"Amari, S.-I., Nagaoka, H.: Methods of information geometry. Translations of Mathematical Monographs, vol.\u00a0191, p. 206. American Mathematical Society, Providence (2000); Translated from the 1993 Japanese original by Daishi Harada"},{"key":"87_CR2","doi-asserted-by":"crossref","unstructured":"Faraut, J., Kor\u00e1nyi, A.: Analysis on symmetric cones. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, Oxford Science Publications, New York (1994)","DOI":"10.1093\/oso\/9780198534778.003.0001"},{"key":"87_CR3","unstructured":"Kakihara, S., Ohara, A., Tsuchiya, T.: Curvature Integrals and Iteration Complexities in SDP and Symmetric Cone Programs. Optimization Online (2011)"},{"issue":"3","key":"87_CR4","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1007\/s10957-012-0180-9","volume":"157","author":"S. Kakihara","year":"2013","unstructured":"Kakihara, S., Ohara, A., Tsuchiya, T.: Information Geometry and Interior-Point Algorithms in Semidefinite Programs and Symmetric Cone Programs. J. Optim. Theory Appl.\u00a0157(3), 749\u2013780 (2013)","journal-title":"J. Optim. Theory Appl."},{"key":"87_CR5","series-title":"Contemp. Math.","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1090\/conm\/114\/1097865","volume-title":"Mathematical Developments Arising from Linear Programming (Brunswick, ME, 1988)","author":"N. Karmarkar","year":"1990","unstructured":"Karmarkar, N.: Riemannian geometry underlying interior-point methods for linear programming. In: Mathematical Developments Arising from Linear Programming (Brunswick, ME, 1988). Contemp. Math., vol.\u00a0114, pp. 51\u201375. Amer. Math. Soc., Providence (1990)"},{"issue":"1, ser. A","key":"87_CR6","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/s10107-007-0141-5","volume":"115","author":"R.D.C. Monteiro","year":"2008","unstructured":"Monteiro, R.D.C., Tsuchiya, T.: A strong bound on the integral of the central path curvature and its relationship with the iteration-complexity of primal-dual path-following LP algorithms. Math. Program.\u00a0115(1, ser. A), 105\u2013149 (2008)","journal-title":"Math. Program."},{"key":"87_CR7","series-title":"SIAM Studies in Applied Mathematics","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1137\/1.9781611970791","volume-title":"Interior-point polynomial algorithms in convex programming","author":"Y. Nesterov","year":"1994","unstructured":"Nesterov, Y., Nemirovskii, A.: Interior-point polynomial algorithms in convex programming. SIAM Studies in Applied Mathematics, vol.\u00a013, p. 405. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1994)"},{"issue":"4","key":"87_CR8","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s102080010032","volume":"2","author":"Y.E. Nesterov","year":"2002","unstructured":"Nesterov, Y.E., Todd, M.J.: On the Riemannian geometry defined by self-concordant barriers and interior-point methods. Found. Comput. Math.\u00a02(4), 333\u2013361 (2002)","journal-title":"Found. Comput. Math."},{"key":"87_CR9","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/0024-3795(94)00348-3","volume":"247","author":"A. Ohara","year":"1996","unstructured":"Ohara, A., Suda, N., Amari, S.-I.: Dualistic differential geometry of positive definite matrices and its applications to related problems. Linear Algebra Appl.\u00a0247, 31\u201353 (1996)","journal-title":"Linear Algebra Appl."},{"key":"87_CR10","doi-asserted-by":"publisher","DOI":"10.1142\/6241","volume-title":"The geometry of Hessian structures.","author":"H. Shima","year":"2007","unstructured":"Shima, H.: The geometry of Hessian structures. World Scientific, Hackensack (2007)"},{"key":"87_CR11","unstructured":"Tanabe, K.: Center flattening transformation and a centered newton method for linear programming. Manuscript Presented at MP Seminar, The Operations Research Society of Japan (1987)"},{"key":"87_CR12","unstructured":"Tanabe, K.: Centered newton methods and differential geometry of optimization. Cooperative Research Report, The Institute of Statistical Mathematics, 89 (1996)"},{"key":"87_CR13","first-page":"32","volume":"303","author":"K. Tanabe","year":"1988","unstructured":"Tanabe, K., Tsuchiya, T.: New geometry of linear programming. Suurikagaku\u00a0303, 32\u201337 (1988) (in Japanese)","journal-title":"Suurikagaku"},{"issue":"1, ser. A","key":"87_CR14","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/BF02592148","volume":"74","author":"S.A. Vavasis","year":"1996","unstructured":"Vavasis, S.A., Ye, Y.: A primal-dual interior point method whose running time depends only on the constraint matrix. Math. Programming\u00a074(1, ser. A), 79\u2013120 (1996)","journal-title":"Math. Programming"}],"container-title":["Lecture Notes in Computer Science","Geometric Science of Information"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-40020-9_87","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T20:10:41Z","timestamp":1715890241000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-40020-9_87"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642400193","9783642400209"],"references-count":14,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-40020-9_87","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}