On the Pseudoconvexity of the Sum of Two Linear Fractional Functions
Charnes and Cooper (1962) reduced a linear fractional program to a linear program with help of a suitable transformation of variables. We show that this transformation preserves pseudoconvexity of a function. The result is then used to characterize sums of two linear fractional functions which are still pseudoconvex. This in turn leads to a characterization of pseudolinear sums of two linear fractional functions.
KeywordsFractional programming sum of ratios pseudoconvexity pseudolinearity
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- Avriel M., Diewert W. E., Schaible S. and Zang I., Generalized concavity, Plenum Press, New York, 1988.Google Scholar
- Cambini A. and Martein L., Generalized concavity and optimality conditions in vector and scalar optimization, “Generalized convexity” (Komlosi et al. eds.), Lect. Notes Econom. Math. Syst., 405, Springer-Verlag, Berlin, 1994, 337–357.Google Scholar
- Cambini R. and Carosi L., On generalized convexity of quadratic fractional functions, Technical Report n.213, Dept. of Statistics and Applied Mathematics, University of Pisa, 2001.Google Scholar
- Craven B. D., Fractional programming, Sigma Ser. Appl. Math. 4, Heldermann Verlag, Berlin, 1988.Google Scholar
- Crouzeix J.P., Characterizations of generalized convexity and monotonicity, a survey, Generalized convexity, generalized monotonicity (Crouzeix et al. eds.), Kluwer Academic Publisher, Dordrecht, 1998, 237–256.Google Scholar
- Martos B., Nonlinear programming theory and methods, North-Holland, Amsterdam, 1975.Google Scholar
- Schaible S., Fractional programming, Handbook of global optimization (Horst and Pardalos eds.), Kluwer Academic Publishers, Dordrecht, 1995, 495–608.Google Scholar