On Monotone Maps: Semidifferentiable Case

Abstract

In this paper, we define the concepts of monotonicity and generalized monotonicity for semidifferentiable maps. Further, we present the characterizations of convexity and generalized convexity in case of semidifferentiable functions. These results rely on general mean-value theorem for semidifferentiable functions (J Glob Optim 40:503–508, 2010). © 2020, Springer Nature Switzerland AG.