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Ray-quasiconvex and f-quasiconvex functions

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Generalized Convexity

Abstract

Using the definition of ray in the euclidean space, we define a new class of functions that avoid Karamardian’s anomaly and which contain the quasimonotonic functions. These new functions have a good behaviour in relation to its optimal sets, allowing the construction of heuristic algorithms in order to find its extreme points.

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References

  1. Beato-Moreno, Mayor-Gallego, Ruiz-Canales (1991): Generalization of non-differentiable convex functions and some characterizations. 14th International Symphosium on Mathematical Programming, Amsterdam, The Netherlands, August 5–9.

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  2. Grennberg and Pierskalla (1971): A review of quasiconvex functions. Operational Research 19. 1553–1570.

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  3. Martos (1975): Non Linear Programming. North-Holland.

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  4. Ruiz-Canales, P. (1986): Estructuras de dominancia definidas por un Cono: Programación Fraccionaria Multiple, Tesis Doctoral. Universidad de Sevilla.

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© 1994 Springer-Verlag Berlin Heidelberg

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Mayor-Gallego, J.A., Rufián-Lizana, A., Ruiz-Canales, P. (1994). Ray-quasiconvex and f-quasiconvex functions. In: Komlósi, S., Rapcsák, T., Schaible, S. (eds) Generalized Convexity. Lecture Notes in Economics and Mathematical Systems, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46802-5_8

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  • DOI: https://doi.org/10.1007/978-3-642-46802-5_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57624-2

  • Online ISBN: 978-3-642-46802-5

  • eBook Packages: Springer Book Archive

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