Karamardian, S.; Schaible, S. Seven kinds of monotone maps. (English) Zbl 0679.90055 J. Optimization Theory Appl. 66, No. 1, 37-46 (1990). Known as well as new types of monotone and generalized monotone maps are considered. For gradient maps, these generalized monotonicity properties can be related to generalized convexity properties of the underlying function. In this way, pure first-order characterizations of various types of generalized convex functions are obtained. Reviewer: S.Karamardian Cited in 8 ReviewsCited in 187 Documents MSC: 90C30 Nonlinear programming 26B25 Convexity of real functions of several variables, generalizations Keywords:generalized monotone maps; first-order characterizations; generalized convex functions PDFBibTeX XMLCite \textit{S. Karamardian} and \textit{S. Schaible}, J. Optim. Theory Appl. 66, No. 1, 37--46 (1990; Zbl 0679.90055) Full Text: DOI References: [1] Karamardian, S.,Complementarity over Cones with Monotone and Pseudomonotone Maps, Journal of Optimization Theory and Applications, Vol. 18, pp. 445-454, 1976. · Zbl 0304.49026 [2] Karamardian, S.,The Nonlinear Complementarity Problem with Applications, Part 2, Journal of Optimization Theory and Applications, Vol. 4, pp. 167-181, 1969. · Zbl 0169.51302 [3] Avriel, M., Diewert, W. E., Schaible, S., andZang, I.,Generalized Concavity, Plenum Publishing Corporation, New York, New York, 1988. [4] Ortega, J. M., andRheinboldt, W. C.,Interactive Solutions of Nonlinear Equations in Several Variables, Academic Press, New York, New York, 1970. [5] Castagnoli, E., andMazzoleni, P.,About Derivatives of Some Generalized Concave Functions, Journal of Information and Optimization Sciences, Vol. 10, pp. 53-64, 1989. · Zbl 0681.90067 [6] Avriel, M., Diewert, W. E., Schaible, S., andZiemba, W. T.,Introduction to Concave and Generalized Concave Functions, Generalized Concavity in Optimization and Economics, Edited by S. Schaible and W. T. Ziemba, Academic Press, New York, New York, pp. 21-50, 1981. · Zbl 0539.90087 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.