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On Monotone Maps: Semidifferentiable Case

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Optimization of Complex Systems: Theory, Models, Algorithms and Applications (WCGO 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 991))

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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).

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Acknowledgements

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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Correspondence to Shashi Kant Mishra .

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Mishra, S.K., Singh, S.K., Shahi, A. (2020). On Monotone Maps: Semidifferentiable Case. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_19

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