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A new tool for the investigation of extended real-valued functions

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Abstract

In this paper, we assign to each extended real-valued function f on a linear space a translative function which is generated by the epigraph of f and called the epitranslative function of f. Relationships between the properties of both functions are investigated. The results are applied to characterize continuity and Lipschitz continuity of f by its epigraph. Furthermore, an epitranslative function is used to derive a formula for the epigraph of the inf-convolution. The basis for the study is established by statements on Gerstewitz functionals and on the directional closure of sets.

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Authors and Affiliations

  1. Faculty of Natural Sciences and Technology, HAWK Hochschule für angewandte Wissenschaft und Kunst Hildesheim/Holzminden/Göttingen, University of Applied Sciences and Arts, Göttingen, Germany

    Petra Weidner

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  1. Petra Weidner
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Correspondence to Petra Weidner.

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Weidner, P. A new tool for the investigation of extended real-valued functions. Optim Lett 13, 1651–1661 (2019). https://doi.org/10.1007/s11590-018-1370-7

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  • DOI: https://doi.org/10.1007/s11590-018-1370-7

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