On the White's algorithm for fractional programming
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https://doi.org/10.33993/jnaat301-688Abstract
In this note we extend for fractional case a method due to White for solving a problem of maximizing over a finite set a function with some special "convexity" properties. Three algorithms applied to a transformation of the initial problem into a maximizing an auxilliary non-fractional function over a bi-product set are given.Downloads
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B. Bereanu, On stochastic linear programming, I: Distribution problems. A simple random variable, Rev. Roumaine Math. Pures Appl., 8 (1963), 683-697.
A. Charnes and W. W. Cooper, Programming with linear fractional functionals, Nav. Res. Log. Quart., 9 (1962), 181-186. DOI: https://doi.org/10.1002/nav.3800090303
W. Dinkelbach, On nonlinear fractional programming, Management Sci., 13 (1967), 492-498, https://doi.org/10.1287/mnsc.13.7.492 DOI: https://doi.org/10.1287/mnsc.13.7.492
I. M. Stancu-Minasian and S. Tigan, On some fractional programming models occurring in minimum risk problems, Lecture Notes in Economics and Mathematical Systems, 345, Managing Editors: M. Beckmann, W. Krelle, A. Cambini, E. Castagnoli, L. Martein, P. Mazoleni, S. Schaible (Eds.), Proc. of the International Workshop on "Generalized Concavity and Economic Applications", Univ. of Pisa, 1988, 295-324, https://doi.org/10.1007/978-3-642-46709-7_22 DOI: https://doi.org/10.1007/978-3-642-46709-7_22
S. Tigan, On some procedure for solving fractional max-min problems, Rev. Anal. Numér. Théor. Approx., 17 (1988), 73-91.
S. Tigan and I. M. Stancu-Minasian, Methods for solving stochastic bilinear fractional max-min problems, Recherche Operationnelle/Operations Research, 30 (1996), 81-98, https://doi.org/10.1051/ro/1996300100811 DOI: https://doi.org/10.1051/ro/1996300100811
S. Tigan, On the maximizing a fractional function over a finite set, in Proceedings of the "Tiberiu Popoviciu" Itinerant Seminar of Functional Equations, Approximation and Convexity, Cluj-Napoca Univ. Babes-Bolyai, E. Popoviciu (ed.), editura SRIMA, Cluj-Napoca, Romania, 2000, 263-270.
D. J. White, A convex form of the quadratic assignment problem, European J. Oper. Res., 65 (1993), 407-416, https://doi.org/10.1016/0377-2217(93)90120-c DOI: https://doi.org/10.1016/0377-2217(93)90120-C
D. J. White, Maximizing a function over a finite set of actions, Technical note, Management Science, 42 (1996), 624-627, https://doi.org/10.1287/mnsc.42.4.624 DOI: https://doi.org/10.1287/mnsc.42.4.624
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