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Characterization of generalized monotone maps. (English) Zbl 0792.90070

Summary: This paper is a sequel to a paper of the first and the second author [J. Optimization Theory Appl. 66, No. 1, 37-46 (1990; Zbl 0697.90067)] in which several kinds of generalized monotonicity were introduced for maps. They were related to generalized convexity properties of functions in the case of gradient maps. In the present paper, we derive first-order characterizations of generalized monotone maps based on a geometrical analysis of generalized monotonicity. These conditions are both necessary and sufficient for generalized monotonicity. Specialized results are obtained for the affine case.

MSC:

90C30 Nonlinear programming
26B25 Convexity of real functions of several variables, generalizations
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