{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T18:25:28Z","timestamp":1775931928393,"version":"3.50.1"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1994,1,1]],"date-time":"1994-01-01T00:00:00Z","timestamp":757382400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[1994,1]]},"DOI":"10.1007\/bf01096535","type":"journal-article","created":{"date-parts":[[2005,2,5]],"date-time":"2005-02-05T04:41:51Z","timestamp":1107578511000},"page":"63-88","source":"Crossref","is-referenced-by-count":88,"title":["Image space analysis of generalized fractional programs"],"prefix":"10.1007","volume":"4","author":[{"given":"James E.","family":"Falk","sequence":"first","affiliation":[]},{"given":"Susan W.","family":"Palocsay","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"CR1","unstructured":"Almogy, Y. and O. Levin (1969), Parametric Analysis of a Multi-Stage Stochastic Shipping Problem,Proc. of the Fifth IFORS Conference, Venice, 359?370."},{"key":"CR2","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1287\/opre.19.1.57","volume":"19","author":"Y. Almogy","year":"1971","unstructured":"Almogy, Y. and O. Levin (1971), A Class of Fractional Programming Problems,Operations Research 19, 57?67.","journal-title":"Operations Research"},{"key":"CR3","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1080\/02522667.1989.10698952","volume":"10","author":"A. Cambini","year":"1989","unstructured":"Cambini, A., L. Martein, and S. Schaible (1989), On Maximizing a Sum of Ratios,Journal of Information and Optimization Sciences 10, 65?79.","journal-title":"Journal of Information and Optimization Sciences"},{"key":"CR4","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1002\/nav.3800090303","volume":"9","author":"A. Charnes","year":"1962","unstructured":"Charnes, A. and W. W. Cooper (1962), Programming with Linear Fractional Functionals,Naval Research Logistics Quarterly 9, 181?186.","journal-title":"Naval Research Logistics Quarterly"},{"key":"CR5","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1287\/mnsc.13.7.492","volume":"13","author":"W. Dinkelbach","year":"1967","unstructured":"Dinkelbach, W. (1967), On Nonlinear Fractional Programming,Management Science 13, 492?498.","journal-title":"Management Science"},{"key":"CR6","first-page":"221","volume-title":"Recent Advances in Global Optimization","author":"J. E. Falk","year":"1992","unstructured":"Falk, J. E. and S. W. Palocsay (1992), Optimizing the Sum of Linear Fractional Functions,Recent Advances in Global Optimization, eds. C. Floudas and M. Pardalos, Princeton University Press: Princeton, New Jersey, 221?258."},{"key":"CR7","doi-asserted-by":"crossref","first-page":"S86","DOI":"10.1287\/opre.40.1.S86","volume":"40","author":"J. E. Falk","year":"1992","unstructured":"Falk, J. E., S. W. Palocsay, W. J. Sacco, W. S. Copes, and H. R. Champion (1992), Bounds on a Trauma Outcome Function via Optimization,Operations Research 40, S86-S95.","journal-title":"Operations Research"},{"key":"CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02598-7","volume-title":"Global Optimization: Deterministic Approaches","author":"R. Horst","year":"1990","unstructured":"Horst, R. and H. Tuy (1990),Global Optimization: Deterministic Approaches, Springer-Verlag: Berlin."},{"key":"CR9","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1287\/mnsc.12.7.609","volume":"12","author":"R. Jagannathan","year":"1966","unstructured":"Jagannathan, R. (1966), On Some Properties of Programming Problems in Parametric Form Pertaining to Fractional Programming,Management Science 12, 609?615.","journal-title":"Management Science"},{"key":"CR10","doi-asserted-by":"crossref","first-page":"143","DOI":"10.15807\/jorsj.32.143","volume":"32","author":"H. Konno","year":"1989","unstructured":"Konno, H. and M. Inori (1989), Bond Portfolio Optimization by Bilinear Fractional Programming,Journal of the Operations Research Society of Japan 32, 143?158.","journal-title":"Journal of the Operations Research Society of Japan"},{"key":"CR11","first-page":"89","volume":"IIISS","author":"H. Konno","year":"1989","unstructured":"Konno, H. and T. Kuno (1989), Linear Multiplicative Programming, Tokyo Institute of Technology Institute of Human and Social Sciences Technical Report IIISS 89?13.","journal-title":"Tokyo Institute of Technology Institute of Human and Social Sciences Technical Report"},{"key":"CR12","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF00120666","volume":"1","author":"H. Konno","year":"1991","unstructured":"Konno, H., Y. Yajima, and T. Matsui (1991), Parametric Simplex Algorithms for Solving a Special Class of Nonconvex Minimization Problems,Journal of Global Optimization 1, 65?81.","journal-title":"Journal of Global Optimization"},{"key":"CR13","first-page":"259","volume-title":"Recent Advances in Global Optimization","author":"H. Konno","year":"1992","unstructured":"Konno, H. and Y. Yajima (1992), Minimizing and Maximizing the Product of Linear Fractional Functions,Recent Advances in Global Optimization, eds. C. Floudas and M. Pardalos, Princeton University Press: Princeton, New Jersey, 259?273."},{"key":"CR14","volume-title":"Nonlinear Programming","author":"O. L. Mangasarian","year":"1969","unstructured":"Mangasarian, O. L. (1969),Nonlinear Programming, McGraw-Hill: New York, New York."},{"key":"CR15","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/S0022-0000(67)80006-0","volume":"1","author":"K. Ritter","year":"1967","unstructured":"Ritter, K. (1967), A Parametric Method for Solving Certain Nonconcave Maximization Problems,Journal of Computer and System Sciences 1, 44?54.","journal-title":"Journal of Computer and System Sciences"},{"key":"CR16","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1002\/nav.3800240416","volume":"24","author":"S. Schaible","year":"1977","unstructured":"Schaible, S. (1977), On the Sum of a Linear and Linear-Fractional Function,Naval Research Logistics Quarterly 24, 691?693.","journal-title":"Naval Research Logistics Quarterly"},{"key":"CR17","first-page":"417","volume-title":"Generalized Concavity in Optimization and Economics","author":"S. Schaible","year":"1981","unstructured":"Schaible, S. (1981), A Survey of Fractional Programming,Generalized Concavity in Optimization and Economics, Academic Press, Inc.: New York, 417?440."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01096535.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01096535\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01096535","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T01:42:12Z","timestamp":1556329332000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01096535"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,1]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1994,1]]}},"alternative-id":["BF01096535"],"URL":"https:\/\/doi.org\/10.1007\/bf01096535","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,1]]}}}