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First-Order Characterizations of Generalized Monotone Maps

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Book cover Operations Research ’91

Abstract

Recently, various kinds of generalized monotonicity were introduced for maps [3]. In case of gradient maps, different types of generalized monotonicity of the gradient correspond to different types of generalized convexity of the underlying function. This gives rise to first-order characterizations of generalized convex functions involving gradients only, not known so far [2].

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References

  1. Arrow, K. J. and A. C. Enthoven, Quasi-concave Programming, Econometrica, 29, pp. 779–800 (1961).

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  2. Avriel, M., W.E. Diewert, S. Schaible and I. Zang, Generalized Concavity, Plenum Publishing Corporation, New York, New York (1988).

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  3. Karamardian, S. and S. Schaible, Seven Kinds of Monotone Maps, Journal of Optimization Theory and Applications, 66, pp. 37–46 (1990).

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  4. Karamardian, S., Schaible, S. and J.P. Crouzeix, Characterizations of Generalized Monotone Maps, Working Paper 90–23, Graduate School of Management, University of California, Riverside (1991).

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  5. Schaible, S. Quasiconvex, Pseudoconvex and Strictly Pseudoconvex Quadratic Functions, Journal of Optimization Theory and Applications 35, pp. 303–338 (1981).

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© 1992 Physica-Verlag Heidelberg

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Schaible, S., Karamardian, S., Crouzeix, JP. (1992). First-Order Characterizations of Generalized Monotone Maps. In: Gritzmann, P., Hettich, R., Horst, R., Sachs, E. (eds) Operations Research ’91. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-48417-9_16

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  • DOI: https://doi.org/10.1007/978-3-642-48417-9_16

  • Publisher Name: Physica-Verlag HD

  • Print ISBN: 978-3-7908-0608-3

  • Online ISBN: 978-3-642-48417-9

  • eBook Packages: Springer Book Archive

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