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Duality in generalized linear fractional programming.(English)Zbl 0526.90083


MSC:

90C32 Fractional programming
49N15 Duality theory (optimization)

Cite

References:

[1]D.J. Ashton and D.R. Atkins, ”Multicriteria programming for financial planning”,Journal of the Operational Research Society 30 (1979) 259–270. ·Zbl 0393.90048
[2]I. Barrodale, ”Best rational approximation and strict quasi-convexity”,SIAM Journal of Numerical Analysis 10 (1973) 8–12. ·Zbl 0262.41034 ·doi:10.1137/0710002
[3]A. Charnes and W.W. Cooper, ”Programming with linear fractional functionals”,Naval Research Logistics Quarterly 9 (1962) 181–186. ·Zbl 0127.36901 ·doi:10.1002/nav.3800090303
[4]A. Charnes and W.W. Cooper, ”Goal programming and multi-objective optimization (Part I)”,European Journal of Operational Research 1 (1977) 39–54. ·Zbl 0375.90079 ·doi:10.1016/S0377-2217(77)81007-2
[5]A. Charnes, L. Cox and M. Lane, ”A Note on the redesigning of a rate structure for allocation of state funds to educational institutions”, Working Paper 70-49 of Project GUM, University of Texas at Austin, (Austin, Texas, 1970).
[6]J.P. Crouzeix, ”Contributions à l’étude des fonctions quasiconvexes”, Doctoral Thesis, Université de Clermont (Clermont, France, 1977).
[7]J.P. Crouzeix, ”A duality framework in quasiconvex programming”, in: S. Schaible and W.T. Ziemba, eds.,Generalized Concavity in Optimization and Economics (Academic Press, New York, 1981) pp. 207–225. ·Zbl 0538.90073
[8]W. Dinkelbach, ”On nonlinear fractional programming”,Management Science 13 (1967) 492–498. ·Zbl 0152.18402 ·doi:10.1287/mnsc.13.7.492
[9]J. Flachs, ”Global saddle-point duality for quasi-concave programs, II”,Mathematical Programming 24 (1982) 326–345. ·Zbl 0493.90070 ·doi:10.1007/BF01585114
[10]E.G. Gol’stein,Theory of convex progranming, Translations of mathematical monographs 36 (American Mathematical Society, Providence, Rhode Island, 1972).
[11]R. Jagannathan, ”On some properties of programming problems in parametric form pertaining to fractional programming”,Management Science 12 (1966) 609–615. ·Zbl 0143.21602 ·doi:10.1287/mnsc.12.7.609
[12]R. Jagannathan and S. Schaible, ”Duality in generalized fractional programming via Farkas Lemma”,Journal of Optimization Theory and Applications, to appear. ·Zbl 0502.90079
[13]J.S.H. Kornbluth, ”A survey of goal programming”,OMEGA 1 (1973) 193–205. ·doi:10.1016/0305-0483(73)90023-6
[14]O.L. Mangasarian,Nonlinear programming (McGraw-Hill, New York, 1969). ·Zbl 0194.20201
[15]U. Passy and A. Keslassy, ”Pseudo duality and duality for explicitly quasiconvex functions”, Mimeograph Series No. 249. Faculty of Industrial Engineering and Management, Technion (Haifa, Israel, 1979). ·Zbl 0496.90075
[16]G.S. Rubinshtein, ”Duality in mathematical programming and some problems of convex analysis”, (English translation)Russian mathematical surveys 25 (1970) 171–200. ·Zbl 0225.90039 ·doi:10.1070/RM1970v025n05ABEH003800
[17]S. Schaible, ”Fractional programming: transformations, duality and algorithmic aspects”, Technical Report 73-9, Department of Operations Research, Stanford University (Stanford, CA, 1973). ·Zbl 0307.26010
[18]S. Schaible, ”Fractional programming I, Duality”,Management Science 22 (1976) 858–867. ·Zbl 0338.90050 ·doi:10.1287/mnsc.22.8.858
[19]S. Schaible, ”Duality in fractional programming: a unified approach”,Operations Research 24 (1976) 452–461. ·Zbl 0348.90120 ·doi:10.1287/opre.24.3.452
[20]S. Schaible,Analyse und Anwendungen von Quotientenprogrammen (Hain-Verlag, Meisenheim, 1978). ·Zbl 0395.90045
[21]S. Schaible, ”A survey of fractional programming”, in: S. Schaible and W.T. Ziemba, eds.,Generalized concavity in optimization and economics (Academic Press, New York, 1981) pp. 417–440. ·Zbl 0535.90092
[22]S. Schaible, ”Bibliography in fractional programming”,Zeitschrift für Operations Research 26 (7) (1982). ·Zbl 0494.90076
[23]E.C. Tammer, ”Dualitätstheorie für hyperbolische und stückweise-lineare konvexe Optimierungs-probleme”,Mathematische Operationenforschung und Statistik 5 (1974) 93–108. ·Zbl 0294.90084
[24]R. Vogt, ”A corporate strategy for realizing equal employment opportunity”,Behavioral and Social Accounting, to appear.
[25]J. von Neumann, ”A model of general economic equilibrium”,Review of Economic Studies 13 (1945) 1–9. ·Zbl 0063.05928 ·doi:10.2307/2296111
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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