On Monotone Maps: Semidifferentiable Case
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).
KeywordsGeneralized convexity Generalized monotonicity First-order conditions Semidifferentials
The first author is financially supported by Department of Science and Technology, SERB, New Delhi, India, through grant no.: MTR/2018/000121. The second author is financially supported by CSIR-UGC JRF, New Delhi, India, through Reference no.: 1272/(CSIR-UGC NET DEC.2016). The third author is financially supported by UGC-BHU Research Fellowship, through sanction letter no: Ref.No./Math/Res/ Sept.2015/2015-16/918.
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