{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:20:20Z","timestamp":1740122420923,"version":"3.37.3"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,6,11]],"date-time":"2019-06-11T00:00:00Z","timestamp":1560211200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,6,11]],"date-time":"2019-06-11T00:00:00Z","timestamp":1560211200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100002701","name":"Ministry of Education","doi-asserted-by":"publisher","award":["NRF 2017-R1A2B2005119"],"award-info":[{"award-number":["NRF 2017-R1A2B2005119"]}],"id":[{"id":"10.13039\/501100002701","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"crossref","award":["KAKENHI (Grant number: 15k00032)"],"award-info":[{"award-number":["KAKENHI (Grant number: 15k00032)"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2019,11]]},"DOI":"10.1007\/s10898-019-00795-w","type":"journal-article","created":{"date-parts":[[2019,6,11]],"date-time":"2019-06-11T05:02:46Z","timestamp":1560229366000},"page":"631-654","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Solving pooling problems with time discretization by LP and SOCP relaxations and rescheduling methods"],"prefix":"10.1007","volume":"75","author":[{"given":"Masaki","family":"Kimizuka","sequence":"first","affiliation":[]},{"given":"Sunyoung","family":"Kim","sequence":"additional","affiliation":[]},{"given":"Makoto","family":"Yamashita","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,6,11]]},"reference":[{"key":"795_CR1","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/j.disopt.2016.04.004","volume":"24","author":"AA Ahmadi","year":"2017","unstructured":"Ahmadi, A.A., Dashb, S., Hal, G.: Optimization over structured subsets of positive semidefinite matrices via column generation. Discrete Optim. 24, 129\u2013151 (2017)","journal-title":"Discrete Optim."},{"key":"795_CR2","doi-asserted-by":"crossref","unstructured":"Ahmadi, A.A. Majumbar, A.: DSOS and SDSOS optimization: Lp and socp-based alternatives to sum of squares optimization. In: Proceedings of the 48th Annual Conference on Information Sciences and Systems, pp. 1\u20135 (2014)","DOI":"10.1109\/CISS.2014.6814141"},{"key":"795_CR3","unstructured":"Ahmadi, A.A., Majumdar, A.: Spotless: software for DSOS and SDSOS optimization (2014). \n                    https:\/\/github.com\/spot-toolbox\/spotless"},{"key":"795_CR4","unstructured":"Alfaki, M.: Models and Solution Methods for the Pooling Problem. Ph.D. thesis, University of Bergen, Department of Informatics, University of Bergen (2012)"},{"key":"795_CR5","doi-asserted-by":"publisher","first-page":"897","DOI":"10.1007\/s10898-012-9875-6","volume":"56","author":"M Alfaki","year":"2013","unstructured":"Alfaki, M., Haugland, D.: Strong formulations for the pooling problem. J. Glob. Optim. 56, 897\u2013916 (2013)","journal-title":"J. Glob. Optim."},{"issue":"1","key":"795_CR6","doi-asserted-by":"publisher","first-page":"15","DOI":"10.2140\/pjm.1975.57.15","volume":"57","author":"GP Barker","year":"1975","unstructured":"Barker, G.P., Carlson, D.: Cones of diagonally dominant matrices. Pac. J. Math. 57(1), 15\u201332 (1975)","journal-title":"Pac. J. Math."},{"issue":"1\u20133","key":"795_CR7","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/BF01582066","volume":"63","author":"A Ben-Tal","year":"1994","unstructured":"Ben-Tal, A., Eiger, G., Gershovitz, V.: Global minimization by reducing the duality gap. Math. Program. 63(1\u20133), 193\u2013212 (1994)","journal-title":"Math. Program."},{"key":"795_CR8","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1287\/ijoc.6.2.207","volume":"6","author":"A Drud","year":"1994","unstructured":"Drud, A.: CONOPT\u2014A large scale GRG code. ORSA J. Comput. 6, 207\u2013216 (1994)","journal-title":"ORSA J. Comput."},{"issue":"12","key":"795_CR9","doi-asserted-by":"publisher","first-page":"5742","DOI":"10.1021\/ie8016048","volume":"48","author":"CE Gounaris","year":"2009","unstructured":"Gounaris, C.E., Misener, R., Floudas, C.A.: Computational comparison of piecewise-linear relaxations for pooling problems. Ind. Eng. Chem. Res. 48(12), 5742\u20135766 (2009)","journal-title":"Ind. Eng. Chem. Res."},{"issue":"3","key":"795_CR10","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1007\/s10898-016-0434-4","volume":"67","author":"A Gupte","year":"2017","unstructured":"Gupte, A., Ahmed, S., Dey, S.S., Cheon, M.S.: Relaxations and discretizations for the pooling problem. J. Glob. Optim. 67(3), 631\u2013669 (2017)","journal-title":"J. Glob. Optim."},{"key":"795_CR11","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1145\/1111237.1111238","volume":"25","author":"CA Haverly","year":"1978","unstructured":"Haverly, C.A.: Studies of the behavior of recursion for the pooling problem. ACM SIGMAP Bull. 25, 19\u201328 (1978)","journal-title":"ACM SIGMAP Bull."},{"key":"795_CR12","unstructured":"IBM. IBM ILOG CPLEX user\u2019s manual. Tech. Rep. (2015)"},{"issue":"3\u20134","key":"795_CR13","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1080\/10556780108805819","volume":"15","author":"S Kim","year":"2001","unstructured":"Kim, S., Kojima, M.: Second order cone programming relaxation of nonconvex quadratic optimization problems. Optim. Methods Softw. 15(3\u20134), 201\u2013224 (2001)","journal-title":"Optim. Methods Softw."},{"key":"795_CR14","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1023\/A:1025794313696","volume":"26","author":"S Kim","year":"2003","unstructured":"Kim, S., Kojima, M.: Exact solutions of some nonconvex quadratic optimization problems via SDP and SOCP relaxations. Comput. Optim. Appl. 26, 143\u2013154 (2003)","journal-title":"Comput. Optim. Appl."},{"key":"795_CR15","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1016\/j.compchemeng.2013.01.016","volume":"53","author":"SP Kolodziej","year":"2013","unstructured":"Kolodziej, S.P., Grossmann, I.E., Furman, K.C., Sawaya, N.W.: A discretization-based approach for the optimization of the multiperiod blend scheduling problem. Comput. Chem. Eng. 53, 122\u2013142 (2013)","journal-title":"Comput. Chem. Eng."},{"issue":"2","key":"795_CR16","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s10898-006-9005-4","volume":"36","author":"L Liberti","year":"2006","unstructured":"Liberti, L., Pantelides, C.C.: An exact reformulation algorithm for large nonconvex NLPs involving bilinear terms. J. Glob. Optim. 36(2), 161\u2013189 (2006)","journal-title":"J. Glob. Optim."},{"issue":"1","key":"795_CR17","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/s10479-017-2407-5","volume":"265","author":"A Marandi","year":"2018","unstructured":"Marandi, A., Dahlc, J., de Klerk, E.: A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem. Ann. Oper. Res. 265(1), 67\u201392 (2018)","journal-title":"Ann. Oper. Res."},{"key":"795_CR18","unstructured":"Marandi, A., de Klerk, E., Dahlc, J.: Solving sparse polynomial optimization problems with chordal structure using the sparse, bounded-degree sum-of-squares hierarchy. Discrete Appl. Math. (to appear) (2018)"},{"key":"795_CR19","unstructured":"MOSEK ApS. Moset optimization toolbox for MATLAB (2019). \n                    https:\/\/docs.mosek.com\/9.0\/toolbox.pdf"},{"key":"795_CR20","unstructured":"Nishi, T.: A semidefinite programming relaxation approach for the pooling problem a semidefinite programming relaxation approach for the pooling problem. Master\u2019s thesis, Kyoto University, Department of Applied Mathematics and Physics, Kyoto University (2010)"},{"key":"795_CR21","unstructured":"Ralph, D.: Nonlinear programming advances in mathematical programming with complementarity constraints. R. Soc. (2007)"},{"issue":"5","key":"795_CR22","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1080\/10556780410001709439","volume":"19","author":"D Ralph","year":"2004","unstructured":"Ralph, D., Wright, S.J.: Some properties of regularization and penalization schemes for mpecs. Optim. Methods Softw. 19(5), 527\u2013556 (2004)","journal-title":"Optim. Methods Softw."},{"key":"795_CR23","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1080\/10556789908805766","volume":"11&12","author":"JF Sturm","year":"1999","unstructured":"Sturm, J.F.: SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11&12, 625\u2013653 (1999)","journal-title":"Optim. Methods Softw."},{"key":"795_CR24","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s10107-002-0347-5","volume":"95","author":"RH T\u00fct\u00fcnc\u00fc","year":"2003","unstructured":"T\u00fct\u00fcnc\u00fc, R.H., Toh, K.C., Todd, M.J.: Solving semidefinite-quadratic-linear programs using SDPT3. Math. Program. 95, 189\u2013217 (2003)","journal-title":"Math. Program."},{"key":"795_CR25","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1017\/S0962492901000071","volume":"10","author":"MJ Todd","year":"2001","unstructured":"Todd, M.J.: Semidefinite optimization. Acta Numer. 10, 515\u2013560 (2001)","journal-title":"Acta Numer."},{"issue":"2","key":"795_CR26","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1145\/1377612.1377619","volume":"35","author":"H Waki","year":"2008","unstructured":"Waki, H., Kim, S., Kojima, M., Muramatsu, M., Sugimoto, H.: Algorithm 883: SparsePOP: a sparse semidefinite programming relaxation of polynomial optimization problems. ACM Trans. Math. Softw. 35(2), 15 (2008)","journal-title":"ACM Trans. Math. Softw."},{"key":"795_CR27","first-page":"687","volume-title":"Handbook on Semidefinite, Conic and Polynomial Optimization","author":"Makoto Yamashita","year":"2011","unstructured":"Yamashita, M., Fujisawa, K., Fukuda, M., Kobayashi, K., Nakata, K., Nakata, M.: Latest developments in the SDPA family for solving large-scale SDPs. In: Handbook on Semidefinite, Conic and Polynomial Optimization, pp. 687\u2013713. Springer, New York (2012)"},{"issue":"4","key":"795_CR28","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1080\/1055678031000118482","volume":"18","author":"M Yamashita","year":"2003","unstructured":"Yamashita, M., Fujisawa, K., Kojima, M.: Implementation and evaluation of SDPA 6.0 (semidefinite programming algorithm 6.0). Optim. Methods Softw. 18(4), 491\u2013505 (2003)","journal-title":"Optim. Methods Softw."},{"key":"795_CR29","volume-title":"Can Semidefinite Programming be a Key Approach to the Pooling Problem?","author":"E Zanni","year":"2013","unstructured":"Zanni, E.: Can Semidefinite Programming be a Key Approach to the Pooling Problem?. University of Edinburgh, Edinburgh (2013)"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-019-00795-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-019-00795-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-019-00795-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T23:13:49Z","timestamp":1591744429000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-019-00795-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,11]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,11]]}},"alternative-id":["795"],"URL":"https:\/\/doi.org\/10.1007\/s10898-019-00795-w","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2019,6,11]]},"assertion":[{"value":"20 February 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 June 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 June 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}