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OnG-semidifferentiable functions in Euclidean spaces

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Abstract

We give a criterion for a functionf:R n →R to be upperG-semidifferentiable in the sense of Ref. 1 at a point\(\bar x \in R^n \). Using this result, we describe upperG-semiderivatives whenG is, for instance, one of the following basic classes of homogeneous functions: the set of all continuous positively homogeneous functions, the set of differences of two sublinear functions, and the set of sublinear functions. As a result, connections between upperG-semidifferentiability and the concepts of differentiability in Refs. 2–4 are obtained.

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Communicated by F. Giannessi

This research was supported by a grant from the World Laboratory. The author would like to thank Professor M. Pappalardo for useful comments.

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Yen, N.D. OnG-semidifferentiable functions in Euclidean spaces. J Optim Theory Appl 85, 377–392 (1995). https://doi.org/10.1007/BF02192233

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