Abstract
Monotonicity plays an important role in complementarity problems and variational inequality problems, like convexity in mathematical programming. Recently, seven kinds of monotone and generalized monotone maps were introduced; see Karamardian et al. (1990). In case of a gradient map, 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, not known so far; see Avriel et al. (1988).
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