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
Arrow, K. J. and A. C. Enthoven, Quasi-concave Programming, Econometrica, 29, pp. 779–800 (1961).
Avriel, M., W.E. Diewert, S. Schaible and I. Zang, Generalized Concavity, Plenum Publishing Corporation, New York, New York (1988).
Karamardian, S. and S. Schaible, Seven Kinds of Monotone Maps, Journal of Optimization Theory and Applications, 66, pp. 37–46 (1990).
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).
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
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