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A General Representation of δ-normal Sets to Sublevels of Convex Functions

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Abstract

The (δ-) normal cone to an arbitrary intersection of sublevel sets of proper, lower semicontinuous, and convex functions is characterized, using either ε-subdifferentials at the nominal point or exact subdifferentials at nearby points. Our tools include (ε-) calculus rules for sup/max functions. The framework of this work is that of a locally convex space, however, formulas using exact subdifferentials require some restriction either on the space (e.g. Banach), or on the function (e.g. epi-pointed).

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Acknowledgements

We would like to thank the reviewers for their careful reading and for providing valuable suggestions which allowed us to improve our manuscript.

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Authors and Affiliations

  1. Center for Mathematical Modeling, Department of Mathematical Engineering, Universidad de Chile, Santiago, Chile

    Abderrahim Hantoute & Anton Svensson

Authors
  1. Abderrahim Hantoute
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  2. Anton Svensson
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Corresponding author

Correspondence to Abderrahim Hantoute.

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Dedicated to Prof. Michel Théra on his 70th birthday

This work is partially supported by CONICYT grant Fondecyt 1151003, Conicyt-Redes no. 150040, and Mathamsud 17-MATH-06.

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Hantoute, A., Svensson, A. A General Representation of δ-normal Sets to Sublevels of Convex Functions. Set-Valued Var. Anal 25, 651–678 (2017). https://doi.org/10.1007/s11228-017-0460-5

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