{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T04:10:40Z","timestamp":1751429440005,"version":"3.41.0"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2002,10,1]],"date-time":"2002-10-01T00:00:00Z","timestamp":1033430400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2002,10,1]],"date-time":"2002-10-01T00:00:00Z","timestamp":1033430400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Global Optimization"],"published-print":{"date-parts":[[2002,10]]},"DOI":"10.1023\/a:1020299805773","type":"journal-article","created":{"date-parts":[[2003,3,15]],"date-time":"2003-03-15T13:37:24Z","timestamp":1047735444000},"page":"237-260","source":"Crossref","is-referenced-by-count":8,"title":["Parallel Implementation of Successive Convex Relaxation Methods for Quadratic Optimization Problems"],"prefix":"10.1007","volume":"24","author":[{"given":"Akiko","family":"Takeda","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Katsuki","family":"Fujisawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yusuke","family":"Fukaya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masakazu","family":"Kojima","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"405658_CR1","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s101079900106","volume":"87","author":"C. Audet","year":"2000","unstructured":"Audet, C., Hansen, P., Jaumard, B. and Savard, G. (2000), A Branch and Cut Algorithm for Nonconvex Quadratically Constrained Quadratic Programming, Mathematical Programming 87, 131\u2013152.","journal-title":"Mathematical Programming"},{"key":"405658_CR2","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/BF01581273","volume":"58","author":"E. Balas","year":"1993","unstructured":"Balas, E., Ceria, S. and Cornuejols, G. (1993), A Lift-and-Project Cutting Plane Algorithm for Mixed 0\u20131 Programs, Mathematical Programming 58, 295\u2013323.","journal-title":"Mathematical Programming"},{"key":"405658_CR3","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1145\/174603.174411","volume":"20","author":"P.H. Calamai","year":"1994","unstructured":"Calamai, P.H. and Vicente, L.N. (1994), Generating Quadratic Bilevel Programming Problems, ACM Transactions on Mathematical Software 20, 103\u2013122.","journal-title":"ACM Transactions on Mathematical Software"},{"key":"405658_CR4","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/BF01582148","volume":"61","author":"P.H. Calamai","year":"1993","unstructured":"Calamai, P.H., Vincente, L.N. and Judice, J.J. (1993), A New Technique for Generating Quadratic Programming Test Problems, Mathematical Programming 61, 215\u2013231.","journal-title":"Mathematical Programming"},{"key":"405658_CR5","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1023\/A:1008282830093","volume":"10","author":"T. Fujie","year":"1997","unstructured":"Fujie, T. and Kojima, M. (1997), Semidefinite Relaxation for Nonconvex Programs, Journal of Global Optimization 10, 367\u2013380.","journal-title":"Journal of Global Optimization"},{"key":"405658_CR6","first-page":"235","volume":"79","author":"K. Fujisawa","year":"1997","unstructured":"Fujisawa, K., Kojima, M. and Nakata, K. (1997), Exploiting Sparsity in Primal-Dual Interior-Point Methods for Semidefinite Programming, Mathematical Programming 79, 235\u2013253.","journal-title":"Mathematical Programming"},{"key":"405658_CR7","volume-title":"User's Manual, Technical Report B-308","author":"K. Fujisawa","year":"1999","unstructured":"Fujisawa, K., Kojima, M. and Nakata, K. (1999), SDPA (Semidefinite Programming Algorithm), User's Manual, Technical Report B-308, Tokyo Institute of Technology, Oh-Okayama, Meguro, Tokyo 152\u20138552, Japan."},{"key":"405658_CR8","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1287\/moor.26.3.519.10580","volume":"26","author":"M. Kojima","year":"2001","unstructured":"Kojima, M. and Takeda, A. (2001), Complexity Analysis of Successive Convex Relaxation Methods for Nonconvex Sets, Mathematics of Operations Research 26, 519\u2013542.","journal-title":"Mathematics of Operations Research"},{"key":"405658_CR9","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1137\/S1052623498336450","volume":"10","author":"M. Kojima","year":"2000","unstructured":"Kojima, M. and Tun\u00e7el, L. (2000), Cones of Matrices and Successive Convex Relaxations of Nonconvex Sets, SIAM Journal on Optimization 10, 750\u2013778.","journal-title":"SIAM Journal on Optimization"},{"key":"405658_CR10","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/PL00011394","volume":"89","author":"M. Kojima","year":"2000","unstructured":"Kojima, M. and Tun\u00e7el, L. (2000), Discretization and Localization in Successive Convex Relaxation Method for Nonconvex Quadratic Optimization Problems, Mathematical Programming 89, 79\u2013111.","journal-title":"Mathematical Programming"},{"key":"405658_CR11","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1137\/0801013","volume":"1","author":"L. Lov\u00e1sz","year":"1991","unstructured":"Lov\u00e1sz, L. and Schrijver, A. (1991), Cones of Matrices and Set Functions and 0\u20131 Optimization, SIAM Journal on Optimization 1, 166\u2013190.","journal-title":"SIAM Journal on Optimization"},{"key":"405658_CR12","volume-title":"Global Optimization","author":"R. Horst","year":"1992","unstructured":"Horst, R. and Tuy, H. (1992), Global Optimization, Second, Revised Edition, Springer, Berlin.","edition":"Second, Revised"},{"key":"405658_CR13","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/BF01580665","volume":"10","author":"G.P. McCormick","year":"1976","unstructured":"McCormick, G.P. (1976), Computability of Global Solutions to Factorable Nonconvex Programs: Part I-Convex Underestimating Problems, Mathematical Programming 10, 147\u2013175.","journal-title":"Mathematical Programming"},{"key":"405658_CR14","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/BF00121268","volume":"8","author":"M.G. Nicholls","year":"1996","unstructured":"Nicholls, M.G. (1996), The Application of Non-Linear Bilevel Programming to the Aluminium Industry, Journal of Global Optimization 8, 245\u2013261.","journal-title":"Journal of Global Optimization"},{"key":"405658_CR15","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/BF02247879","volume":"45","author":"P.M. Pardalos","year":"1990","unstructured":"Pardalos, P.M. and Rodgers, G. (1990), Computational Aspects of a Branch and Bound Algorithm for Quadratic 0\u20131 Programming, Computing 45, 131\u2013144.","journal-title":"Computing"},{"key":"405658_CR16","first-page":"843","volume":"1","author":"P.M. Pardalos","year":"1991","unstructured":"Pardalos, P.M. and Vavasis, S.A. (1991), Quadratic Programming with One Negative Eigenvalue is NP-Hard, Journal of Global Optimization 1, 843\u2013855.","journal-title":"Journal of Global Optimization"},{"key":"405658_CR17","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/BF00138689","volume":"8","author":"H.S. Ryoo","year":"1996","unstructured":"Ryoo, H.S. and Sahinidis, N.V. (1996), A Branch-and-Reduce Approach to Global Optimization, Journal of Global Optimization 8, 107\u2013139.","journal-title":"Journal of Global Optimization"},{"key":"405658_CR18","volume-title":"High-Performance Computing and Networking, Lecture Notes in Computing Science","author":"M. Sato","year":"1997","unstructured":"Sato, M., Nakada, H., Sekiguchi, S., Matsuoka, S., Nagashima, U. and Takagi, H. (1997), Ninf: A Network Based Information Library for a Global World-Wide Computing Infrastructure, in Sloot, P. and Hertzberger, B. (eds.), High-Performance Computing and Networking, Lecture Notes in Computing Science, Vol. 1225, Springer, Berlin."},{"key":"405658_CR19","unstructured":"S. Sekiguchi, Sato, M., Nakada, H., Matsuoka, S. and Nagashima, U. (1996), Ninf: Network Based Information Library for Globally Performance Computing, in Proc. of Parallel Object-Oriented Methods and Applications (POOMA\u2019 96)."},{"key":"405658_CR20","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1137\/0403036","volume":"3","author":"H.D. Sherali","year":"1990","unstructured":"Sherali, H.D. and Adams, W.P. (1990), A Hierarchy of Relaxations Between the Continuous and Convex Hull Representations for Zero-One Programming Problems, SIAM Journal on Discrete Mathematics 3, 411\u2013430.","journal-title":"SIAM Journal on Discrete Mathematics"},{"key":"405658_CR21","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/BF00122429","volume":"2","author":"H.D. Sherali","year":"1992","unstructured":"Sherali, H.D. and Alameddine, A. (1992), A New Reformulation-Linearization Technique for Bilinear Programming Problems, Journal of Global Optimization 2, 379\u2013410.","journal-title":"Journal of Global Optimization"},{"key":"405658_CR22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01100203","volume":"7","author":"H.D. Sherali","year":"1995","unstructured":"Sherali, H.D. and Tuncbilek, C.H. (1995), A Reformulation-Convexification Approach for Solving Nonconvex Quadratic Programming Problems, Journal of Global Optimization 7, 1\u201331.","journal-title":"Journal of Global Optimization"},{"key":"405658_CR23","volume-title":"Technical Report 96\u201301","author":"R.A. Stubbs","year":"1997","unstructured":"Stubbs, R.A. and Mehrotra, S. (1997), A Branch-and-Cut Method for 0\u20131 Mixed Convex Programming, Technical Report 96\u201301, Dept. of IE\/MS, Northwestern University, Evanston, IL 60208."},{"key":"405658_CR24","volume-title":"Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems","author":"A. Takeda","year":"2000","unstructured":"Takeda, A., Dai, Y., Fukuda, M. and Kojima, M. (2000), Towards the Implementation of Successive Convex Relaxation Method for Nonconvex Quadratic Optimization Problems, in Pardalos, P.M. (ed.), Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems, Kluwer Academic Publishers, Dordrecht."},{"key":"405658_CR25","volume-title":"Applications and Algorithms of Complementarity","author":"A. Takeda","year":"2000","unstructured":"Takeda, A. and Kojima, M. (2000), Successive Convex Relaxation Approach to Bilevel Quadratic Optimization Problems, in Ferris, M.C., Mangasarian, O.L. and Pang, J.S. (eds.), Applications and Algorithms of Complementarity, Kluwer Academic Publishers, Dordrecht."},{"key":"405658_CR26","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/BF01096458","volume":"5","author":"L.N. Vicente","year":"1994","unstructured":"Vicente, L.N. and Calamai, P.H. (1994), Bilevel and Multilevel Programming: A Bibliography Review, Journal of Global Optimization 5, 291\u2013306.","journal-title":"Journal of Global Optimization"},{"key":"405658_CR27","volume-title":"State of the Art in Global Optimization","author":"V. Visweswaran","year":"1996","unstructured":"Visweswaran, V., Floudas, C.A., Ierapetritou, M.G. and Pistikopoulos, E.N. (1996), A Decomposition-Based Global Optimization Approach for Solving Bilevel Linear and Quadratic Programs, in Floudas, C.A. and Pardalos, P.M. (eds.), State of the Art in Global Optimization, Kluwer Academic Publishers, Dordrecht."},{"key":"405658_CR28","volume-title":"State of the Art in Global Optimization","author":"T.V. Voorhis","year":"1996","unstructured":"Voorhis, T.V. and Al-khayyal, F. (1996), Accelerating Convergence of Branch-and-Bound Algorithms for Quadrically Constrained Optimization Problems, in Floudas, C.A. and Pardalos, P.M. (1996), State of the Art in Global Optimization, Kluwer Academic Publishers, Dordrecht."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1020299805773.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1020299805773\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1020299805773.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:45:30Z","timestamp":1751366730000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1020299805773"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,10]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2002,10]]}},"alternative-id":["405658"],"URL":"https:\/\/doi.org\/10.1023\/a:1020299805773","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2002,10]]}}}