Abstract
This paper is a sequel to Ref. 1 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.
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Karamardian, S., Schaible, S. & Crouzeix, J.P. Characterizations of generalized monotone maps. J Optim Theory Appl 76, 399–413 (1993). https://doi.org/10.1007/BF00939374
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DOI: https://doi.org/10.1007/BF00939374