{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T16:24:14Z","timestamp":1761582254322,"version":"3.37.3"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T00:00:00Z","timestamp":1675382400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T00:00:00Z","timestamp":1675382400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11704336","11701512"],"award-info":[{"award-number":["11704336","11701512"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2023,5]]},"DOI":"10.1007\/s10589-023-00452-9","type":"journal-article","created":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T12:03:03Z","timestamp":1675425783000},"page":"247-261","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A simultaneous diagonalization based SOCP relaxation for portfolio optimization with an orthogonality constraint"],"prefix":"10.1007","volume":"85","author":[{"given":"Zhijun","family":"Xu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0291-6464","authenticated-orcid":false,"given":"Jing","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,2,3]]},"reference":[{"issue":"6","key":"452_CR1","doi-asserted-by":"publisher","first-page":"73","DOI":"10.2469\/faj.v46.n6.73","volume":"46","author":"RD Arnott","year":"1990","unstructured":"Arnott, R.D., Wagner, W.H.: The measurement and control of trading costs. Financ. Anal. J. 46(6), 73\u201380 (1990)","journal-title":"Financ. Anal. J."},{"key":"452_CR2","first-page":"469","volume":"81","author":"R Baviera","year":"2021","unstructured":"Baviera, R., Bianchi, G.: Model risk in mean-variance portfolio selection: an analytic solution to the worst-case approach. Optim. Lett. 81, 469\u2013491 (2021)","journal-title":"Optim. Lett."},{"issue":"1\u20132","key":"452_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10107-013-0710-8","volume":"143","author":"A Ben-Tal","year":"2014","unstructured":"Ben-Tal, A., Den Hertog, D.: Hidden conic quadratic representation of some nonconvex quadratic optimization problems. Math. Program. 143(1\u20132), 1\u201329 (2014)","journal-title":"Math. Program."},{"key":"452_CR4","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1023\/A:1021806200854","volume":"24","author":"MJ Best","year":"2003","unstructured":"Best, M.J., Hlouskova, J.: Portfolio selection and transactions costs. Comput. Optim. Appl. 24, 95\u2013116 (2003)","journal-title":"Comput. Optim. Appl."},{"key":"452_CR5","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s10589-013-9618-8","volume":"59","author":"S Burer","year":"2014","unstructured":"Burer, S., Kim, S., Kojima, M.: Faster, but weaker, relaxations for quadratically constrained quadratic programs. Comput. Optim. Appl. 59, 27\u201345 (2014)","journal-title":"Comput. Optim. Appl."},{"key":"452_CR6","unstructured":"Braun, S.E.: Solving a quadratic programming problem subject to orthogonality constraints. Ph.D. thesis, Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY (2001)"},{"issue":"1","key":"452_CR7","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10589-005-1014-6","volume":"31","author":"S Braun","year":"2005","unstructured":"Braun, S., Mitchell, J.E.: A semidefinite programming heuristic for quadratic programming problems with complementarity constraints. Comput. Optim. Appl. 31(1), 5\u201329 (2005)","journal-title":"Comput. Optim. Appl."},{"issue":"2","key":"452_CR8","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1007\/s11590-015-0931-2","volume":"10","author":"TP Dinh","year":"2015","unstructured":"Dinh, T.P., Thi, H., Pham, V.N., Niu, Y.S.: DC programming approaches for discrete portfolio optimization under concave transaction costs. Optim. Lett. 10(2), 261\u2013282 (2015)","journal-title":"Optim. Lett."},{"issue":"3","key":"452_CR9","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1287\/opre.2013.1170","volume":"61","author":"J Gao","year":"2013","unstructured":"Gao, J., Li, D.: Optimal cardinality constrained portfolio selection. Oper. Res. 61(3), 745\u2013761 (2013)","journal-title":"Oper. Res."},{"key":"452_CR10","unstructured":"Gillett, P.L.: Semidefinite programming approaches and software tools for quadratic programs with linear complementarity constraints. Ph.D. thesis, Engineering Mathematics, Polytechnique Montreal, Quebec (2016)"},{"key":"452_CR11","doi-asserted-by":"publisher","first-page":"1074","DOI":"10.1016\/j.ejor.2021.03.023","volume":"295","author":"S Guo","year":"2021","unstructured":"Guo, S., Gu, J.W., Ching, W.K.: Adaptive online portfolio selection with transaction costs. Eur. J. Oper. Res. 295, 1074\u20131086 (2021)","journal-title":"Eur. J. Oper. Res."},{"key":"452_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2020.102353","volume":"102","author":"J Gonz\u00e1lez-D\u00edaz","year":"2021","unstructured":"Gonz\u00e1lez-D\u00edaz, J., Gonz\u00e1lez-Rodr\u00edguez, B., Leal, M., Puerto, J.: Global optimization for bilevel portfolio design: economic insights from the Dow Jones index. Omega Int. J. Manag. Sci. 102, 102353 (2021)","journal-title":"Omega Int. J. Manag. Sci."},{"key":"452_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2021.105582","volume":"138","author":"VN Katsikis","year":"2022","unstructured":"Katsikis, V.N., Mourtas, S.D., Stanimirovi, P.S., Li, S., Gao, X.: Time-varying mean-variance portfolio selection problem solving via LVI-PDNN. Comput. Oper. Res. 138, 105582 (2022)","journal-title":"Comput. Oper. Res."},{"key":"452_CR14","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, 201\u2013224 (2001)","journal-title":"Optim. Methods Softw."},{"issue":"2","key":"452_CR15","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1016\/j.ejor.2013.10.060","volume":"234","author":"PN Kolm","year":"2014","unstructured":"Kolm, P.N., T\u00fct\u00fcnc\u00fc, R., Fabozzi, F.J.: 60 Years of portfolio optimization: practical challenges and current trends. Eur. J. Oper. Res. 234(2), 356\u2013371 (2014)","journal-title":"Eur. J. Oper. Res."},{"key":"452_CR16","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1023\/A:1013850928936","volume":"22","author":"H Konno","year":"2002","unstructured":"Konno, H., Wijayanayake, K.A.: Portfolio optimization under D.C. transaction costs and minimal transaction unit constraints. J. Glob. Optim. 22, 137\u2013152 (2002)","journal-title":"J. Glob. Optim."},{"issue":"1","key":"452_CR17","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1007\/s10957-015-0856-z","volume":"170","author":"Z Landsman","year":"2016","unstructured":"Landsman, Z., Makov, U.: Minimization of a function of a quadratic functional with application to optimal portfolio selection. J. Optim. Theory Appl. 170(1), 308\u2013322 (2016)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"452_CR18","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/s10107-005-0582-7","volume":"103","author":"J Linderoth","year":"2005","unstructured":"Linderoth, J.: A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs. Math. Program. 103(2), 251\u2013282 (2005)","journal-title":"Math. Program."},{"key":"452_CR19","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/s10479-006-0145-1","volume":"152","author":"MS Lobo","year":"2007","unstructured":"Lobo, M.S., Fazel, M., Boyd, S.: Portfolio optimization with linear and fixed transaction costs. Ann. Oper. Res. 152, 341\u2013365 (2007)","journal-title":"Ann. Oper. Res."},{"issue":"1","key":"452_CR20","first-page":"77","volume":"7","author":"HM Markowitz","year":"1952","unstructured":"Markowitz, H.M.: Portfolio selection. J. Finance 7(1), 77\u201391 (1952)","journal-title":"J. Finance"},{"issue":"1","key":"452_CR21","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1007\/s10479-013-1461-x","volume":"223","author":"S Marzban","year":"2015","unstructured":"Marzban, S., Mahootchi, M., Khamseh, A.A.: Developing a multi-period robust optimization model considering American style options. Ann. Oper. Res. 223(1), 305\u2013320 (2015)","journal-title":"Ann. Oper. Res."},{"key":"452_CR22","unstructured":"Mittelmann, H.D.: Several SDP-codes on sparse and other SDP problems. http:\/\/plato.asu.edu\/ftp\/sparse_sdp.html. Accessed 27 Dec 2022"},{"issue":"2","key":"452_CR23","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1090\/qam\/124336","volume":"19","author":"RW Newcomb","year":"1961","unstructured":"Newcomb, R.W.: On the simultaneous diagonalization of two semi-definite matrices. Q. Appl. Math. 19(2), 144\u2013146 (1961)","journal-title":"Q. Appl. Math."},{"issue":"23","key":"452_CR24","first-page":"1119","volume":"4","author":"J Wang","year":"2010","unstructured":"Wang, J., Lu, J., Feng, Y.: Congruence diagonalization of two hermite matrices simultaneously. Int. J. Algebra 4(23), 1119\u20131125 (2010)","journal-title":"Int. J. Algebra"},{"issue":"1","key":"452_CR25","first-page":"135","volume":"233","author":"H Ying","year":"2014","unstructured":"Ying, H., Ng, K., Huang, B., Huang, H.: Portfolio optimization with transaction costs: a two-period mean-variance model. Ann. Oper. Res. 233(1), 135\u2013156 (2014)","journal-title":"Ann. Oper. Res."},{"key":"452_CR26","first-page":"99","volume":"39","author":"A Yoshimoto","year":"1996","unstructured":"Yoshimoto, A.: The mean-variance approach to portfolio optimization subject to transaction costs. J. Oper. Res. Soc. Jpn. 39, 99\u2013117 (1996)","journal-title":"J. Oper. Res. Soc. Jpn."},{"issue":"2","key":"452_CR27","first-page":"1","volume":"17","author":"Y Zhang","year":"2017","unstructured":"Zhang, Y., Xiang, L., Guo, S.: Portfolio selection problems with Markowitz\u2019s mean-variance framework: a review of literature. Fuzzy Optim. Decis. Mak. 17(2), 1\u201334 (2017)","journal-title":"Fuzzy Optim. Decis. Mak."},{"issue":"7","key":"452_CR28","doi-asserted-by":"publisher","first-page":"1615","DOI":"10.1007\/s11590-018-1337-8","volume":"13","author":"J Zhou","year":"2019","unstructured":"Zhou, J., Xu, Z.: A simultaneous diagonalization based SOCP relaxation for convex quadratic programs with linear complementarity constraints. Optim. Lett. 13(7), 1615\u20131630 (2019)","journal-title":"Optim. Lett."},{"issue":"9","key":"452_CR29","doi-asserted-by":"publisher","first-page":"2529","DOI":"10.1080\/02331934.2020.1865347","volume":"71","author":"J Zhou","year":"2022","unstructured":"Zhou, J., Chen, S., Yu, S., Tian, Y.: A simultaneous diagonalization based quadratic convex reformulation for nonconvex quadratically constrained quadratic program. Optimization 71(9), 2529\u20132545 (2022)","journal-title":"Optimization"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-023-00452-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10589-023-00452-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-023-00452-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,5]],"date-time":"2023-04-05T16:47:31Z","timestamp":1680713251000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10589-023-00452-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,3]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,5]]}},"alternative-id":["452"],"URL":"https:\/\/doi.org\/10.1007\/s10589-023-00452-9","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"type":"print","value":"0926-6003"},{"type":"electronic","value":"1573-2894"}],"subject":[],"published":{"date-parts":[[2023,2,3]]},"assertion":[{"value":"5 January 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 January 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 February 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}