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Sublevel representations of epi-Lipschitz sets and other properties

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Abstract

Epi-Lipschitz sets in normed spaces are represented as sublevel sets of Lipschitz functions satisfying a so-called qualification condition. Canonical representations through the signed distance functions associated with the sets are also obtained. New optimality conditions are provided, for optimization problems with epi-Lipschitz set constraints, in terms of the signed distance function.

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Notes

  1. Hiriart-Urruty [11] formally states the result in a Banach space. The proof is obviously valid in any normed space.

  2. Again, stated in a Banach space, and valid in any normed space.

  3. As the author notices in [16], the argument in [15], written in finite dimensions, remains valid in any normed space.

  4. In a Banach space, the argument in [11] is valid in any normed space.

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Authors and Affiliations

  1. Institut Montpelliérain Alexander Grothendieck, UMR 5149 CNRS, Université de Montpellier, 34095, Montpellier, France

    Marc-Olivier Czarnecki & Lionel Thibault

  2. Centro de Modelamiento Matematico, Universidad de Chile, Santiago, Chile

    Lionel Thibault

Authors
  1. Marc-Olivier Czarnecki
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  2. Lionel Thibault
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Correspondence to Lionel Thibault.

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Czarnecki, MO., Thibault, L. Sublevel representations of epi-Lipschitz sets and other properties. Math. Program. 168, 555–569 (2018). https://doi.org/10.1007/s10107-016-1070-y

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  • DOI: https://doi.org/10.1007/s10107-016-1070-y

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