{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:46:41Z","timestamp":1760028401507},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2022,1]]},"DOI":"10.1007\/s10957-021-01980-2","type":"journal-article","created":{"date-parts":[[2022,1,6]],"date-time":"2022-01-06T00:03:39Z","timestamp":1641427419000},"page":"360-378","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Adaptive Global Algorithm for Solving Box-Constrained Non-convex Quadratic Minimization Problems"],"prefix":"10.1007","volume":"192","author":[{"given":"Amar","family":"Andjouh","sequence":"first","affiliation":[]},{"given":"Mohand Ouamer","family":"Bibi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,1,6]]},"reference":[{"key":"1980_CR1","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1023\/A:1008293029350","volume":"13","author":"Y Ajima","year":"1998","unstructured":"Ajima, Y., Fujie, T.: A polyhedral approach for nonconvex quadratic programming problems with box constraints. J. Glob. Optim. 13, 151\u2013170 (1998)","journal-title":"J. Glob. Optim."},{"key":"1980_CR2","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1023\/A:1008278114178","volume":"10","author":"MJ Best","year":"1997","unstructured":"Best, M.J., Ding, B.: Global and local quadratic minimization. J. Glob. Optim. 10, 77\u201390 (1997)","journal-title":"J. Glob. Optim."},{"issue":"2","key":"1980_CR3","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1504\/IJMOR.2020.105862","volume":"16","author":"MO Bibi","year":"2020","unstructured":"Bibi, M.O., Ikeneche, N., Bentobache, M.: A hybrid direction algorithm for solving a convex quadratic problem. Int. J. Math. Oper. Res. 16(2), 159\u2013178 (2020)","journal-title":"Int. J. Math. Oper. Res."},{"key":"1980_CR4","doi-asserted-by":"publisher","first-page":"826","DOI":"10.1137\/0803042","volume":"3","author":"IM Bomze","year":"1993","unstructured":"Bomze, I.M., Danninger, G.: A global optimization algorithm for concave quadratic programming problems. SIAM J. Optim. 3, 826\u2013842 (1993)","journal-title":"SIAM J. Optim."},{"key":"1980_CR5","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1080\/02331930902878341","volume":"59","author":"B Brahmi","year":"2010","unstructured":"Brahmi, B., Bibi, M.O.: Dual Support method for Solving convex quadratic programs. Optimization 59, 851\u2013872 (2010)","journal-title":"Optimization"},{"key":"1980_CR6","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/s00186-007-0173-x","volume":"67","author":"R Cambini","year":"2008","unstructured":"Cambini, R., Sodini, C.: A sequential method for a class of box constrained quadratic programming problems. Math. Meth. Oper. Res. 67, 223\u2013243 (2008)","journal-title":"Math. Meth. Oper. Res."},{"key":"1980_CR7","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s12532-011-0033-9","volume":"4","author":"J Chen","year":"2012","unstructured":"Chen, J., Burer, S.: Globally solving nonconvex quadratic programming problems via completely positive programming. Math. Prog. Comp. 4, 33\u201352 (2012)","journal-title":"Math. Prog. Comp."},{"key":"1980_CR8","doi-asserted-by":"publisher","first-page":"1040","DOI":"10.1137\/S1052623494240456","volume":"6","author":"TF Coleman","year":"1996","unstructured":"Coleman, T.F., Li, Y.: A reflective newton method for minimizing a quadratic function subject to bounds on some of the variables. SIAM J. Optim. 6, 1040\u20131058 (1996)","journal-title":"SIAM J. Optim."},{"key":"1980_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/PL00011369","volume":"88","author":"TF Coleman","year":"2000","unstructured":"Coleman, T.F., Li, Y.: A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints. Math. Prog. Ser. A 88, 1\u201331 (2000)","journal-title":"Math. Prog. Ser. A"},{"key":"1980_CR10","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1023\/A:1018990014974","volume":"18","author":"L Fernandes","year":"1998","unstructured":"Fernandes, L., Fischer, A., Judice, J., Requejo, C., Soares, J.: A block active set algorithm for large-scale quadratic programing with box constraints. Ann. Oper. Res. 18, 75\u201395 (1998)","journal-title":"Ann. Oper. Res."},{"key":"1980_CR11","volume-title":"Constructive Methods of Optimization: Part 4: Convex Problems","author":"R Gabasov","year":"1987","unstructured":"Gabasov, R., Kirillova, F.M., Kostyukova, O.I., Raketsky, V.M.: Constructive Methods of Optimization: Part 4: Convex Problems. University Press, Minsk (1987)"},{"key":"1980_CR12","volume-title":"Practical Optimization","author":"PE Gill","year":"1981","unstructured":"Gill, P.E., Murray, W., Wright, M.H.: Practical Optimization. Academic Press, London (1981)"},{"key":"1980_CR13","first-page":"1","volume":"5","author":"S Gratton","year":"2020","unstructured":"Gratton, S., Simon, E., Toint, P.L.: An algorithm for the minimization of nonsmooth nonconvex functions using inexact evaluations and its worst-case complexity. Math. Prog. 5, 1\u201324 (2020)","journal-title":"Math. Prog."},{"key":"1980_CR14","first-page":"474","volume":"3","author":"CG Han","year":"1992","unstructured":"Han, C.G., Pardalos, P.M., Ye, Y.: On the solution of indefinite quadratic problems using an interior-point algorithm. Informatica 3, 474\u2013496 (1992)","journal-title":"Informatica"},{"key":"1980_CR15","volume-title":"Introduction to Global Optimization","author":"R Horst","year":"1995","unstructured":"Horst, R., Pardalos, P.M., Thoai, N.V.: Introduction to Global Optimization. Kluwer Academic Publishers, Dordrecht (1995)"},{"key":"1980_CR16","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1007\/s10898-006-9022-3","volume":"36","author":"V Jeyakumar","year":"2006","unstructured":"Jeyakumar, V., Rubinov, A.M., Wu, Z.Y.: Sufficient global optimality conditions for nonconvex quadratic minimization problems with box constraints. J. Glob. Optim. 36, 471\u2013481 (2006)","journal-title":"J. Glob. Optim."},{"key":"1980_CR17","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1007\/s10957-007-9185-1","volume":"132","author":"V Jeyakumar","year":"2007","unstructured":"Jeyakumar, V., Rubinov, A.M., Wu, Z.Y.: Generalized Fenchel\u2019s conjugation formulas and duality for abstract convex functions. J. Optim. Theory Appl. 132, 441\u2013458 (2007)","journal-title":"J. Optim. Theory Appl."},{"key":"1980_CR18","first-page":"960","volume":"41","author":"EA Kostina","year":"2001","unstructured":"Kostina, E.A., Kostyukova, O.I.: An algorithm for solving quadratic programming problems with linear equality and inequality constraints. Comput. Math. Math. Phys. 41, 960\u2013973 (2001)","journal-title":"Comput. Math. Math. Phys."},{"key":"1980_CR19","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1023\/A:1008288411710","volume":"11","author":"HA Le Thi","year":"1997","unstructured":"Le Thi, H.A., Pham Dinh, T.: Solving a class of linearly constrained indefinite quadratic problems by DC algorithms. J. Glob. Optim. 11, 253\u2013285 (1997)","journal-title":"J. Glob. Optim."},{"key":"1980_CR20","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/s10957-018-1345-y","volume":"179","author":"HA Le Thi","year":"2018","unstructured":"Le Thi, H.A., Huynh, V.N., Pham Dinh, T.: Convergence analysis of difference-of-convex algorithm with subanalytic data. J. Optim. Theory Appl. 179, 103\u2013126 (2018)","journal-title":"J. Optim. Theory Appl."},{"key":"1980_CR21","doi-asserted-by":"publisher","first-page":"985","DOI":"10.1007\/s11590-017-1203-0","volume":"12","author":"C Lu","year":"2018","unstructured":"Lu, C., Deng, Z.: DC decomposition based branch-and-bound algorithms for box-constrained quadratic programs. Optim. Lett. 12, 985\u2013996 (2018)","journal-title":"Optim. Lett."},{"key":"1980_CR22","doi-asserted-by":"publisher","first-page":"658","DOI":"10.1016\/j.cam.2010.01.003","volume":"234","author":"Y Lua","year":"2010","unstructured":"Lua, Y., Pang, L.P., Liang, X.J., Xia, Z.Q.: An approximate decomposition algorithm for convex minimization. J. Comput. Appl. Math. 234, 658\u2013666 (2010)","journal-title":"J. Comput. Appl. Math."},{"key":"1980_CR23","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1007\/s10898-005-3845-1","volume":"34","author":"OL Mangasarian","year":"2006","unstructured":"Mangasarian, O.L., Rosen, J.B., Thompson, M.E.: Nonconvex piecewise-quadratic underestimation for global minimization. J. Glob. Optim. 34, 475\u2013488 (2006)","journal-title":"J. Glob. Optim."},{"key":"1980_CR24","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1137\/0804009","volume":"4","author":"JM Martinez","year":"1994","unstructured":"Martinez, J.M.: Local minimizers of quadratic functions on Euclidean balls and spheres. SIAM J. Optim. 4, 159\u2013176 (1994)","journal-title":"SIAM J. Optim."},{"key":"1980_CR25","first-page":"851","volume":"59","author":"PM Pardalos","year":"1991","unstructured":"Pardalos, P.M.: Global optimization algorithms for linearly constrained indefinite quadratic problems. Comput. Math. Appl. 59, 851\u2013872 (1991)","journal-title":"Comput. Math. Appl."},{"key":"1980_CR26","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1145\/103147.103156","volume":"17","author":"PM Pardalos","year":"1991","unstructured":"Pardalos, P.M.: Construction of test problems in quadratic bivalent programming. Math. Softw. 17, 74\u201387 (1991)","journal-title":"Math. Softw."},{"key":"1980_CR27","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/BF00120662","volume":"1","author":"PM Pardalos","year":"1991","unstructured":"Pardalos, P.M., Vavasis, S.A.: Quadratic programming with one negative eigenvalue is NP-hard. J. Glob. Optim. 1, 15\u201322 (1991)","journal-title":"J. Glob. Optim."},{"issue":"4","key":"1980_CR28","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1080\/10556780802263990","volume":"23","author":"T Pham Dinh","year":"2008","unstructured":"Pham Dinh, T., Le Thi, H.A., Akoa, F.: Combining DCA and interior point techniques for large-scale nonconvex quadratic programming. Optim. Method Softw. 23(4), 609\u2013629 (2008)","journal-title":"Optim. Method Softw."},{"issue":"2","key":"1980_CR29","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1023\/B:JOTA.0000042530.24671.80","volume":"122","author":"MC Pinar","year":"2004","unstructured":"Pinar, M.C.: Sufficient global optimality conditions for bivalent quadratic optimization. J. Optim. Theory Appl. 122(2), 433\u2013440 (2004)","journal-title":"J. Optim. Theory Appl."},{"key":"1980_CR30","first-page":"1525","volume":"6","author":"S Radjef","year":"2012","unstructured":"Radjef, S., Bibi, M.O.: An effective generalization of the direct support method in quadratic convex programming. Appl. Math. Sci. 6, 1525\u20131540 (2012)","journal-title":"Appl. Math. Sci."},{"key":"1980_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3200-9","volume-title":"Abstract Convexity and Global Optimization","author":"AM Rubinov","year":"2000","unstructured":"Rubinov, A.M.: Abstract Convexity and Global Optimization. Kluwer Academic, Dordrecht (2000)"},{"issue":"3","key":"1980_CR32","doi-asserted-by":"publisher","first-page":"904","DOI":"10.1007\/s10957-012-0041-6","volume":"154","author":"HN Tuan","year":"2012","unstructured":"Tuan, H.N.: Convergence rate of the Pham Dinh-Le Thi algorithm for the trust-region subproblem. J. Optim. Theory Appl. 154(3), 904\u2013915 (2012)","journal-title":"J. Optim. Theory Appl."},{"key":"1980_CR33","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1007\/s10107-004-0550-7","volume":"102","author":"D Vandenbussche","year":"2005","unstructured":"Vandenbussche, D., Nemhauser, G.L.: A branch-and-cut algorithm for nonconvex quadratic programs with box constraints. Math. Prog. 102, 559\u2013575 (2005)","journal-title":"Math. Prog."},{"key":"1980_CR34","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/s10898-007-9147-z","volume":"39","author":"ZY Wu","year":"2007","unstructured":"Wu, Z.Y.: Sufficient global optimality conditions for weakly convex minimization problems. J. Glob. Optim 39, 427\u2013440 (2007)","journal-title":"J. Glob. Optim"},{"key":"1980_CR35","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/s10957-007-9177-1","volume":"133","author":"ZY Wu","year":"2007","unstructured":"Wu, Z.Y., Jeyakumar, V., Rubinov, A.M.: Sufficient conditions for globally optimality of bivalent nonconvex quadratic programs. J. Optim. Theory Appl. 133, 123\u2013130 (2007)","journal-title":"J. Optim. Theory Appl."},{"key":"1980_CR36","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1007\/s10957-009-9616-2","volume":"145","author":"ZY Wu","year":"2010","unstructured":"Wu, Z.Y., Rubinov, A.M.: Global optimality conditions for some classes of optimization problems. J. Optim. Theory Appl. 145, 164\u2013185 (2010)","journal-title":"J. Optim. Theory Appl."},{"key":"1980_CR37","first-page":"95","volume":"353","author":"SN Yi","year":"2019","unstructured":"Yi, S.N., Joaquim, J., An, L.T.H., Tao, P.D.: Improved DC programming approaches for solving the quadratic eigenvalue complementarity problem. Appl. Math. Comput. 353, 95\u2013113 (2019)","journal-title":"Appl. Math. Comput."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-021-01980-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-021-01980-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-021-01980-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,21]],"date-time":"2022-01-21T12:34:16Z","timestamp":1642768456000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-021-01980-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["1980"],"URL":"https:\/\/doi.org\/10.1007\/s10957-021-01980-2","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1]]},"assertion":[{"value":"4 March 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 November 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 January 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}