{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T14:16:28Z","timestamp":1772547388413,"version":"3.50.1"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T00:00:00Z","timestamp":1713398400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T00:00:00Z","timestamp":1713398400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2024,5]]},"DOI":"10.1007\/s10957-024-02406-5","type":"journal-article","created":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T05:01:56Z","timestamp":1713416516000},"page":"631-667","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The Nonconvex Second-Order Cone: Algebraic Structure Toward Optimization"],"prefix":"10.1007","volume":"201","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1839-8083","authenticated-orcid":false,"given":"Baha","family":"Alzalg","sequence":"first","affiliation":[]},{"given":"Lilia","family":"Benakkouche","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,18]]},"reference":[{"key":"2406_CR1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10107-002-0339-5","volume":"95","author":"F Alizadeh","year":"2003","unstructured":"Alizadeh, F., Goldfarb, D.: Second-order cone programming. Math. Program. 95, 3\u201351 (2003)","journal-title":"Math. Program."},{"key":"2406_CR2","first-page":"1","volume":"249","author":"B Alzalg","year":"2014","unstructured":"Alzalg, B.: Decomposition-based interior point methods for stochastic quadratic second-order cone programming. Appl. Math. Comput. 249, 1\u201318 (2014)","journal-title":"Appl. Math. Comput."},{"key":"2406_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.7153\/oam-11-01","volume":"11","author":"B Alzalg","year":"2017","unstructured":"Alzalg, B.: The Jordan algebraic structure of the circular cone. Oper. Matrices 11, 1\u201321 (2017)","journal-title":"Oper. Matrices"},{"key":"2406_CR4","doi-asserted-by":"publisher","first-page":"2291","DOI":"10.1080\/02331934.2018.1533553","volume":"67","author":"B Alzalg","year":"2018","unstructured":"Alzalg, B.: Primal interior-point decomposition algorithms for two-stage stochastic extended second-order cone programming. Optimization 67, 2291\u20132323 (2018)","journal-title":"Optimization"},{"key":"2406_CR5","doi-asserted-by":"publisher","first-page":"3522","DOI":"10.1109\/ACCESS.2021.3139915","volume":"10","author":"B Alzalg","year":"2022","unstructured":"Alzalg, B., Alioui, H.: Applications of stochastic mixed-integer second-order cone optimization. IEEE Access 10, 3522\u20133547 (2022)","journal-title":"IEEE Access"},{"key":"2406_CR6","doi-asserted-by":"publisher","first-page":"2245","DOI":"10.1080\/02331934.2017.1360888","volume":"66","author":"B Alzalg","year":"2017","unstructured":"Alzalg, B., Pirhaji, M.: Elliptic cone optimization and primal-dual path-following algorithms. Optimization 66, 2245\u20132274 (2017)","journal-title":"Optimization"},{"key":"2406_CR7","doi-asserted-by":"publisher","first-page":"5122","DOI":"10.1016\/j.apm.2011.12.053","volume":"36","author":"BM Alzalg","year":"2012","unstructured":"Alzalg, B.M.: Stochastic second-order cone programming: applications models. Appl. Math. Model. 36, 5122\u20135134 (2012)","journal-title":"Appl. Math. Model."},{"key":"2406_CR8","unstructured":"Alzalg, B., Benakkouche, L.: Functions associated with the nonconvex second-order cone. Submitted for publication (2023)"},{"key":"2406_CR9","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/s10589-007-9089-x","volume":"40","author":"HY Benson","year":"2008","unstructured":"Benson, H.Y., Shanno, D.F.: Interior-point methods for nonconvex nonlinear programming: regularization and warmstarts. Comput. Optim. Appl. 40, 143\u2013189 (2008)","journal-title":"Comput. Optim. Appl."},{"key":"2406_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04245-8","volume-title":"Computational Geometry","author":"M de Berg","year":"2000","unstructured":"de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.C.: Voronoi diagrams. In: Computational Geometry. Springer, Berlin, Heidelberg (2000)"},{"key":"2406_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-34395-0","volume-title":"Alg\u00e8bre: Chapitres 1 \u00e0 3","author":"N Bourbaki","year":"2007","unstructured":"Bourbaki, N.: Alg\u00e8bre: Chapitres 1 \u00e0 3. Springer (2007)"},{"key":"2406_CR12","doi-asserted-by":"publisher","DOI":"10.1017\/9781108770385","volume-title":"Spacetime and Geometry: An Introduction to General Relativity","author":"S Carroll","year":"2019","unstructured":"Carroll, S.: Spacetime and Geometry: An Introduction to General Relativity. Cambridge University Press, Cambridge (2019)"},{"key":"2406_CR13","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1080\/02331930600819514","volume":"55","author":"J-Sh Chen","year":"2006","unstructured":"Chen, J.-Sh.: The convex and monotone functions associated with second-order cone. Optimization 55, 363\u2013385 (2006)","journal-title":"Optimization"},{"key":"2406_CR14","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S1052623402417298","volume":"1","author":"R Correa","year":"2004","unstructured":"Correa, R.: A global algorithm for nonlinear semidefinite programming. SIAM J. Optim. 1, 303\u2013318 (2004)","journal-title":"SIAM J. Optim."},{"key":"2406_CR15","doi-asserted-by":"publisher","first-page":"3447","DOI":"10.1137\/090747634","volume":"32","author":"FE Curtis","year":"2010","unstructured":"Curtis, F.E., Schenk, O., W\u00e4chter, A.: An interior-point algorithm for large-scale nonlinear optimization with inexact step computations. SIAM J. Sci. Comput. 32, 3447\u20133475 (2010)","journal-title":"SIAM J. Sci. Comput."},{"key":"2406_CR16","doi-asserted-by":"crossref","unstructured":"Faraut, J., Gindikin, S.: Pseudo-Hermitian symmetric spaces of tube type. In: Memory of Jozef D\u2019atri (ed.): Topics in Geometry, pp 123\u2013154. Springer (1996)","DOI":"10.1007\/978-1-4612-2432-7_3"},{"key":"2406_CR17","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198534778.001.0001","volume-title":"Analysis on Symmetric Cones","author":"J Faraut","year":"1994","unstructured":"Faraut, J., Kor\u00e1nyi, A.: Analysis on Symmetric Cones. The Clarendon Press, Oxford University Press, New York (1994)"},{"key":"2406_CR18","doi-asserted-by":"publisher","first-page":"1132","DOI":"10.1137\/S1052623496305560","volume":"8","author":"A Forsgren","year":"1998","unstructured":"Forsgren, A., Gill, Ph.E.: Primal-dual interior methods for nonconvex nonlinear programming. SIAM J. Optim. 8, 1132\u20131152 (1998)","journal-title":"SIAM J. Optim."},{"key":"2406_CR19","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1007\/s10107-006-0028-x","volume":"109","author":"RW Freund","year":"2007","unstructured":"Freund, R.W., Jarre, F., Vogelbusch, Ch.H.: Nonlinear semidefinite programming: sensitivity, convergence, and an application in passive reduced-order modeling. Math. Program. 109, 581\u2013611 (2007)","journal-title":"Math. Program."},{"key":"2406_CR20","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/s10957-021-01962-4","volume":"193","author":"Y Gao","year":"2022","unstructured":"Gao, Y., Nemeth, S.Z., Sznajder, R.: The monotone extended second-order cone and mixed complementarity problems. J. Optim. Theory Appl. 193, 381\u2013407 (2022)","journal-title":"J. Optim. Theory Appl."},{"key":"2406_CR21","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s00186-011-0350-9","volume":"74","author":"R Garc\u00e9s","year":"2011","unstructured":"Garc\u00e9s, R., G\u00f3mez, W., Jarre, F.: A self-concordance property for nonconvex semidefinite programming. Math. Oper. Res. 74, 77\u201392 (2011)","journal-title":"Math. Oper. Res."},{"key":"2406_CR22","doi-asserted-by":"publisher","first-page":"1096","DOI":"10.1007\/s11232-009-0102-7","volume":"160","author":"SS Gershtein","year":"2009","unstructured":"Gershtein, S.S., Logunov, A.A., Mestvirishvili, M.A.: Gravitational waves in the relativistic theory of gravity. Theor. Math. Phys. 160, 1096\u20131100 (2009)","journal-title":"Theor. Math. Phys."},{"key":"2406_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1070\/RM1964v019n04ABEH001153","volume":"19","author":"SG Gindikin","year":"1964","unstructured":"Gindikin, S.G.: Analysis inhomogeneous domains. Russ. Math. Surv. 19, 1\u201389 (1964)","journal-title":"Russ. Math. Surv."},{"key":"2406_CR24","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817","volume-title":"Matrix Analysis","author":"RA Horn","year":"1985","unstructured":"Horn, R.A., Johnson, Ch.R.: Matrix Analysis. Cambridge University Press (1985)"},{"key":"2406_CR25","doi-asserted-by":"publisher","first-page":"577","DOI":"10.36890\/iejg.1274663","volume":"16","author":"A Kizilay","year":"2023","unstructured":"Kizilay, A., Yakut, A.T.: Inextensible flows of space curves according to a new orthogonal frame with curvature in $${\\mathbb{E} }_{1}^{3}$$. Int. Electron. J. Geom. 16, 577\u2013593 (2023)","journal-title":"Int. Electron. J. Geom."},{"key":"2406_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0096285","volume-title":"The Minnesota Notes on Jordan Algebras and Their Applications","author":"M Koecher","year":"1999","unstructured":"Koecher, M.: The Minnesota Notes on Jordan Algebras and Their Applications. Springer (1999)"},{"key":"2406_CR27","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/s11005-023-01692-w","volume":"113","author":"E Minguzzi","year":"2023","unstructured":"Minguzzi, E.: Lorentzian manifolds properly isometrically embeddable in Minkowski spacetime. Lett. Math. Phys. 113, 67 (2023)","journal-title":"Lett. Math. Phys."},{"key":"2406_CR28","doi-asserted-by":"crossref","unstructured":"Moradi, E., Bidkhori, M.: Single Facility Location Problem. In: Zanjirani Farahani, R., Hekmatfar, M. (eds.) Facility Location. Contributions to Management Science. Physica, Heidelberg (2009)","DOI":"10.1007\/978-3-7908-2151-2_3"},{"key":"2406_CR29","doi-asserted-by":"crossref","unstructured":"N\u00e9meth, S.Z.: Zhang, G,: Extended Lorentz cones and mixed complementarity problems. J. Glob. Optim. 62, 443\u2013457 (2015)","DOI":"10.1007\/s10898-014-0259-y"},{"key":"2406_CR30","doi-asserted-by":"publisher","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, Philadelpha (1994)"},{"key":"2406_CR31","unstructured":"Neuenhofen, M.: Weakly polynomial efficient minimization of a non-convex quadratic function with logarithmic barriers in a trust-region. arXiv preprint arXiv:1806.06936 (2018)"},{"key":"2406_CR32","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1287\/moor.1080.0315","volume":"34","author":"H Qi","year":"2009","unstructured":"Qi, H.: Local duality of nonlinear semidefinite programming. Math. Oper. Res. 34, 124\u2013141 (2009)","journal-title":"Math. Oper. Res."},{"key":"2406_CR33","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/0024-3795(94)00124-3","volume":"236","author":"M Renardy","year":"1996","unstructured":"Renardy, M.: Singular value decomposition in Minkowski space. Linear Algebra Appl. 236, 53\u201358 (1996)","journal-title":"Linear Algebra Appl."},{"key":"2406_CR34","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/s10107-003-0380-z","volume":"96","author":"SH Schmieta","year":"2003","unstructured":"Schmieta, S.H., Alizadeh, F.: Extension of primal-dual interior point algorithms to symmetric cones. Math. Program. 96, 409\u2013438 (2003)","journal-title":"Math. Program."},{"key":"2406_CR35","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/s101070050116","volume":"87","author":"DF Shanno","year":"2000","unstructured":"Shanno, D.F., Vanderbei, R.J.: Interior-point methods for nonconvex nonlinear programming: orderings and higher-order methods. Math. Program. 87, 303\u2013316 (2000)","journal-title":"Math. Program."},{"key":"2406_CR36","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1287\/moor.1060.0195","volume":"31","author":"D Sun","year":"2006","unstructured":"Sun, D.: The strong second-order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications. Math. Oper. Res. 31, 761\u2013776 (2006)","journal-title":"Math. Oper. Res."},{"key":"2406_CR37","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/s10479-011-0861-z","volume":"186","author":"W Sun","year":"2011","unstructured":"Sun, W., Li, Ch., Sampaio, R.J.B.: On duality theory for non-convex semidefinite programming. Ann. Oper. Res. 186, 331\u2013343 (2011)","journal-title":"Ann. Oper. Res."},{"issue":"1","key":"2406_CR38","doi-asserted-by":"publisher","first-page":"5","DOI":"10.2307\/2024512","volume":"65","author":"H Stein","year":"1968","unstructured":"Stein, H.: On Einstein\u2013Minkowski space-time. J. Philos. 65(1), 5\u201323 (1968)","journal-title":"J. Philos."},{"key":"2406_CR39","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492901000071","volume-title":"Semidefinite Optimization","author":"MJ Todd","year":"2001","unstructured":"Todd, M.J.: Semidefinite Optimization. Cambridge University Press, Acta Numerica (2001)"},{"key":"2406_CR40","doi-asserted-by":"crossref","unstructured":"Tuy, H.: Nonconvex quadratic programming. In Memory of Jozef D\u2019atri (ed.): Convex Analysis and Global Optimization, pp 337\u2013390. Springer (2016)","DOI":"10.1007\/978-3-319-31484-6_10"},{"key":"2406_CR41","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1023\/A:1008677427361","volume":"13","author":"RJ Vanderbei","year":"1999","unstructured":"Vanderbei, R.J., Shanno, D.F.: An interior-point algorithm for nonconvex nonlinear programming. Comput. Optim. Appl. 13, 231\u2013252 (1999)","journal-title":"Comput. Optim. Appl."},{"key":"2406_CR42","doi-asserted-by":"publisher","first-page":"104964","DOI":"10.1016\/j.biosystems.2023.104964","volume":"231","author":"O Witkowski","year":"2023","unstructured":"Witkowski, O., Doctor, T., Solomonova, E., Duane, B., Levin, M.: Towards an ethics of autopoietic technology: stress, care, and intelligence. Biosystems 231, 104964 (2023)","journal-title":"Biosystems"},{"key":"2406_CR43","doi-asserted-by":"publisher","first-page":"899","DOI":"10.1080\/02331934.2013.848861","volume":"63","author":"L Zhang","year":"2014","unstructured":"Zhang, L., Li, Y., Wu, J.: Nonlinear rescaling Lagrangians for nonconvex semidefinite programming. Optim. 63, 899\u2013920 (2014)","journal-title":"Optim."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-024-02406-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-024-02406-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-024-02406-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T15:16:18Z","timestamp":1715267778000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-024-02406-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,18]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,5]]}},"alternative-id":["2406"],"URL":"https:\/\/doi.org\/10.1007\/s10957-024-02406-5","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,18]]},"assertion":[{"value":"10 August 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 February 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 April 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}