{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T21:03:41Z","timestamp":1780434221062,"version":"3.54.1"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2000,11,1]],"date-time":"2000-11-01T00:00:00Z","timestamp":973036800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2000,11,1]],"date-time":"2000-11-01T00:00:00Z","timestamp":973036800000},"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":[[2000,11]]},"DOI":"10.1023\/a:1008314922240","type":"journal-article","created":{"date-parts":[[2002,12,22]],"date-time":"2002-12-22T14:41:38Z","timestamp":1040568098000},"page":"283-299","source":"Crossref","is-referenced-by-count":71,"title":["A Branch and Bound Algorithm for Solving Low Rank Linear Multiplicative and Fractional Programming Problems"],"prefix":"10.1007","volume":"18","author":[{"given":"Hiroshi","family":"Konno","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kenji","family":"Fukaishi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"270960_CR1","unstructured":"Almogy, Y. and Levin, O. (1964), Parametric Analysis of a Multi-Stage Stochastic Shipping Problem, Proc. of the Fifth IFORS Conference, Venice, 359-370."},{"key":"270960_CR2","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1287\/moor.8.2.273","volume":"8","author":"F. Al-Khayyol","year":"1983","unstructured":"Al-Khayyol, F. and Falk, J.E. (1983), Jointly Constrained Bi-convex Programming, Mathematics of Operations Research 8: 273-286.","journal-title":"Mathematics of Operations Research"},{"key":"270960_CR3","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/BF01099647","volume":"7","author":"I.P. Androulakis","year":"1995","unstructured":"Androulakis, I.P., Maranas, C.D. and Floudas, C.A. (1995), \u03b1BB: A Global Optimization Method for General Constrained Nonconvex Problems, J. of Global Optimization 7: 337-363.","journal-title":"J. of Global Optimization"},{"key":"270960_CR4","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1080\/02522667.1989.10698957","volume":"10","author":"A. Cambini","year":"1989","unstructured":"Cambini, A., Martein, L. and Schaible, S. (1989), On Maximizing the Sum of Ratios, J. of Information and Optimization Science 10: 141-151.","journal-title":"J. of Information and Optimization Science"},{"key":"270960_CR5","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1002\/nav.3800090303","volume":"9","author":"A. Charnes","year":"1962","unstructured":"Charnes, A. and Cooper, W.W. (1962), Programming with Linear Fractional Functions, Naval Research Logistics 9: 181-186.","journal-title":"Naval Research Logistics"},{"key":"270960_CR6","volume-title":"Fractional Programming","author":"B.D. Craver","year":"1988","unstructured":"Craver, B.D. (1988), Fractional Programming, Heldermann-Verlag, Berlin."},{"key":"270960_CR7","doi-asserted-by":"crossref","unstructured":"Falk, J.E. and Polacsay, S.W. (1992), Optimizing the Sum of Linear Fractional Fuctions in (Floudas and Pardalos eds.), Recent Advances in Global Optimization, Princeton University Press, 221-258.","DOI":"10.1515\/9781400862528.221"},{"key":"270960_CR8","unstructured":"Hirsche, J. (1995), Optimizing of Sum and Products of Linear Fractional Function under Linear Constraints, Technical Report 3, Department of Computer Science and Scientific Computing, Martin-Luther-Universitat."},{"key":"270960_CR9","unstructured":"Horst, R., Pardalos, P.M. and Thoai, N.V. (1995), Introduction to Global Optimization, Kluwer Academic Publishers."},{"key":"270960_CR10","doi-asserted-by":"crossref","unstructured":"Horst, R. and Tuy, H. (1996), Global Optimization: Deterministic Approach (3rd edn.), Springer-Verlag.","DOI":"10.1007\/978-3-662-03199-5_1"},{"key":"270960_CR11","doi-asserted-by":"crossref","unstructured":"Konno, H., Thach, P.T. and Tuy, H. (1997), Optimization on Low Rank Nonconvex Structures, Kluwer Academic Publishers.","DOI":"10.1007\/978-1-4615-4098-4"},{"key":"270960_CR12","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1023\/A:1008376731013","volume":"4","author":"H. Konno","year":"1999","unstructured":"Konno, H. and Abe, N. (1999), Minimization of the Sum of Three Linear Fractional Functions, J. of Global Optimization 4: 419-432.","journal-title":"J. of Global Optimization"},{"key":"270960_CR13","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/BF01580893","volume":"56","author":"H. Konno","year":"1992","unstructured":"Konno, H. and Kuno, T. (1992), Linear Multiplicative Programming, Mathematical Programming 56: 51-64.","journal-title":"Mathematical Programming"},{"key":"270960_CR14","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/BF01096534","volume":"4","author":"H. Konno","year":"1994","unstructured":"Konno, H., Kuno, T. and Yajima, Y. (1994), Global Minimization of a Generalized Convex Multiplicative Function, J. of Global Optimizaton 4: 47-62.","journal-title":"J. of Global Optimizaton"},{"key":"270960_CR15","doi-asserted-by":"crossref","first-page":"295","DOI":"10.15807\/jorsj.39.295","volume":"39","author":"H. Konno","year":"1994","unstructured":"Konno, H. and Watanabe, H. (1994), Bond Portfolio Optimization Problems and Their Applications to Index Tracking, J. of the Operation Reseach Social of Japan 39: 295-306.","journal-title":"J. of the Operation Reseach Social of Japan"},{"key":"270960_CR16","doi-asserted-by":"crossref","unstructured":"Konno, H. and Yajima, Y. (1992), Minimizing and Maximizing the Product of Linear Fractional Functions, in Floudas and Pardalos (eds)., Recent Advances in Global Optimization, Princeton University Press, 259-273.","DOI":"10.1515\/9781400862528.259"},{"key":"270960_CR17","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1002\/(SICI)1520-6750(199908)46:5<583::AID-NAV8>3.0.CO;2-5","volume":"46","author":"H. Konno","year":"1999","unstructured":"Konno, H. and Yamashita, H. (1999), Minimization of the Sum and the Product of Several Linear Fractional Functions, Naval Research Logistics 46: 583-596.","journal-title":"Naval Research Logistics"},{"key":"270960_CR18","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/BF00119935","volume":"1","author":"T. Kuno","year":"1991","unstructured":"Kuno, T. and Konno, H. (1991), A Parametric Successive Underestimation Method for Convex Multiplicative Programming Problems, J. of Global Optimization 1: 267-286.","journal-title":"J. of Global Optimization"},{"key":"270960_CR19","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/BF00121658","volume":"9","author":"T. Matsui","year":"1996","unstructured":"Matsui, T. (1996), NP-Hardness of Linear Multiplicative Programming and Related Problems, J. of Global Optimization 9: 113-119.","journal-title":"J. of Global Optimization"},{"key":"270960_CR20","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0167-6377(95)00014-B","volume":"17","author":"T.Q. Phong","year":"1995","unstructured":"Phong, T.Q., An, L.T.H. and Tao, P.D. (1995), On Globally Solving Linearly Constrained Indefinite Quadratic Minimization Problems by Decomposition Branch and Bound Method, Operations Research Letters 17: 215-220.","journal-title":"Operations Research Letters"},{"key":"270960_CR21","unstructured":"Schaible, S. (1992), Some Recent Results in Fractional Programming, in P. Mazzolevi (ed.), Generalized Convexity for Economic Application, Proc. of the Workshop held in Pisa."},{"key":"270960_CR22","first-page":"223","volume":"8","author":"H. Swarup","year":"1966","unstructured":"Swarup, H. (1966), Programming with Indefinite Quadratic Function with Linear Constraints, Cahier du Coutre d'Etudes de Recherche Operationelle 8: 223-234.","journal-title":"Cahier du Coutre d'Etudes de Recherche Operationelle"},{"key":"270960_CR23","doi-asserted-by":"crossref","unstructured":"Tuy, H. (1998), Convex Analysis and Global Optimization, Kluwer Academic Publishers.","DOI":"10.1007\/978-1-4757-2809-5"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1008314922240.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1008314922240\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1008314922240.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:40:14Z","timestamp":1751366414000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1008314922240"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,11]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2000,11]]}},"alternative-id":["270960"],"URL":"https:\/\/doi.org\/10.1023\/a:1008314922240","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,11]]}}}