{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T09:34:23Z","timestamp":1743154463990,"version":"3.40.3"},"publisher-location":"Singapore","reference-count":18,"publisher":"Springer Singapore","isbn-type":[{"type":"print","value":"9789811050640"},{"type":"electronic","value":"9789811050657"}],"license":[{"start":{"date-parts":[[2017,7,26]],"date-time":"2017-07-26T00:00:00Z","timestamp":1501027200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"DOI":"10.1007\/978-981-10-5065-7_13","type":"book-chapter","created":{"date-parts":[[2017,7,25]],"date-time":"2017-07-25T09:58:39Z","timestamp":1500976719000},"page":"239-255","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Mixed Integer Quadratic Formulation for the Shortest Vector Problem"],"prefix":"10.1007","author":[{"given":"Keiji","family":"Kimura","sequence":"first","affiliation":[]},{"given":"Hayato","family":"Waki","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,7,26]]},"reference":[{"unstructured":"T. Achterberg, Constraint Integer Programming, Ph.D. thesis, Technische Universit\u00e4t Berlin (2007)","key":"13_CR1"},{"unstructured":"T.\u00a0Achterberg, R.E.\u00a0Bixby, Z.\u00a0Gu, E.\u00a0Rothberg, D.\u00a0Weninger, Multi-row presolve reductions in mixed integer programming, in Proceedings of the Twenty-Sixth RAMP Symposium (2014), pp. 181\u2013196","key":"13_CR2"},{"unstructured":"M.\u00a0Ajtai, The shortest vector problem in \n                    \n                      \n                    \n                    $$L_2$$\n                   is NP-hard for randomized reductions (extended abstract), in Proceedings of the thirtieth Annual Symposium on the Theory of Computing (1998), pp. 10\u201319","key":"13_CR3"},{"unstructured":"M.\u00a0Ajtai, R.\u00a0Kumar, D.\u00a0Sivakumar, A sieve algorithm for the shortest lattice vector problem, in Proceedings of the Thirty-third Annual ACM Symposium on Theory of Computing (2001), pp. 601\u2013610","key":"13_CR4"},{"key":"13_CR5","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10107-002-0339-5","volume":"95","author":"F Alizadeh","year":"2003","unstructured":"F. Alizadeh, D. Goldfarb, Second-order cone programming. Math. Program. 95, 3\u201351 (2003)","journal-title":"Math. Program."},{"unstructured":"C. Bliek, P. Bonami, A. Lodi, Solving mixed-integer quadratic programming problems with IBM-CPLEX: a progress report, in Proceedings of the Twenty-Sixth RAMP Symposium (2014), pp. 171\u2013180","key":"13_CR6"},{"key":"13_CR7","first-page":"1","volume":"23","author":"M Fukase","year":"2015","unstructured":"M. Fukase, K. Kashiwabara, An accelerated algorithm for solving SVP based on statistical analysis. J. Inf. Process. 23, 1\u201315 (2015)","journal-title":"J. Inf. Process."},{"doi-asserted-by":"publisher","unstructured":"A.M. Gleixner, T. Bertholdm, B.M\u00fcller, S. Weltge, Three enhancements for optimization-based bound tightening. J. Glob. Optim. (2016). doi:\n                    10.1007\/s10898-016-0450-4","key":"13_CR8","DOI":"10.1007\/s10898-016-0450-4"},{"key":"13_CR9","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/BF01457454","volume":"261","author":"AK Lenstra","year":"1982","unstructured":"A.K. Lenstra, H.W. Lenstra Jr., L. Lov\u00e1sz, Factoring polynomials with rational coefficients. Math. Ann. 261, 515\u2013534 (1982)","journal-title":"Math. Ann."},{"unstructured":"G. Pataki, Strong duality in conic linear programming: facial reduction and extended dual, in Computational and Analytical Mathematics, vol. 50, ed. By D. Bailey et al. Springer Proceedings in Mathematics & Statistics (2013), pp. 613\u2013634","key":"13_CR10"},{"doi-asserted-by":"crossref","unstructured":"J.\u00a0Renegar, A mathematical view of interior-point methods in convex optimization. SIAM (2001)","key":"13_CR11","DOI":"10.1137\/1.9780898718812"},{"key":"13_CR12","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/BF01581144","volume":"66","author":"CP Schnorr","year":"1994","unstructured":"C.P. Schnorr, M. Euchner, Lattice basis reduction: improved practical algorithms and solving subset sum problems. Math. program. 66, 181\u2013199 (1994)","journal-title":"Math. program."},{"key":"13_CR13","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1007\/s10957-012-0219-y","volume":"158","author":"H Waki","year":"2013","unstructured":"H. Waki, M. Muramatsu, Facial reduction algorithms for conic optimization problems. J. Optim. Theory Appl. 158, 188\u2013215 (2013)","journal-title":"J. Optim. Theory Appl."},{"unstructured":"IBM ILOG CPLEX Optimizer 12.6.3, IBM ILOG (2015)","key":"13_CR14"},{"unstructured":"The FPLLL development team, fplll, a lattice reduction library (2016), \n                    https:\/\/github.com\/fplll\/fplll","key":"13_CR15"},{"unstructured":"Gurobi Optimization, Inc., Gurobi Optimizer Reference Manual (2015), \n                    http:\/\/www.gurobi.com","key":"13_CR16"},{"unstructured":"SCIP: Solving Constraint Integer Programs, \n                    http:\/\/scip.zib.de\/","key":"13_CR17"},{"unstructured":"SVP CHALLENGE, \n                    https:\/\/www.latticechallenge.org\/svp-challenge\/","key":"13_CR18"}],"container-title":["Mathematics for Industry","Mathematical Modelling for Next-Generation Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-10-5065-7_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T09:17:49Z","timestamp":1557998269000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-981-10-5065-7_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,26]]},"ISBN":["9789811050640","9789811050657"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-981-10-5065-7_13","relation":{},"ISSN":["2198-350X","2198-3518"],"issn-type":[{"type":"print","value":"2198-350X"},{"type":"electronic","value":"2198-3518"}],"subject":[],"published":{"date-parts":[[2017,7,26]]},"assertion":[{"value":"26 July 2017","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}