Abstract
In this chapter, we introduce the concept of strong pseudomonotonicity and strong quasimonotonicity of set-valued maps of higher order. Non-differentiable strong pseudoconvex/quasiconvex functions of higher order are characterized by the strong pseudomonotonicity/quasimonotonicity of their corresponding set-valued maps. As a by-product, we solve the open problem (converse part of Proposition 6.2) of Karamardian and Schaible (J. Optim. Theory Appl. 66:37–46, 1990) for the more general case as strong pseudoconvexity for non-smooth, locally Lipschitz continuous functions.
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Acknowledgements
The authors are indebted to anonymous referees for valuable comments and suggestions which led to the present improved version as it stands.
The first author is financially supported by CSIR-UGC JRF, New Delhi, India, through reference no. 1272/(CSIR-UGC NET DEC.2016). The second author is financially supported by UGC-BHU Research Fellowship, through sanction letter no. Ref. No./Math/Res/Sept.2015/2015-16/918. The third author is financially supported by the Department of Science and Technology, SERB, New Delhi, India, through grant no. MTR/2018/000121.
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Singh, S.K., Shahi, A., Kant Mishra, S. (2021). Strong Pseudoconvexity and Strong Quasiconvexity of Non-differentiable Functions. In: Singh, V.K., Sergeyev, Y.D., Fischer, A. (eds) Recent Trends in Mathematical Modeling and High Performance Computing. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-68281-1_15
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DOI: https://doi.org/10.1007/978-3-030-68281-1_15
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