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Conditioning and Upper-Lipschitz Inverse Subdifferentials in Nonsmooth Optimization Problems

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Abstract

In this paper, we study conditioning problems for convex and nonconvex functions defined on normed linear spaces. We extend the notion of upper Lipschitzness for multivalued functions introduced by Robinson, and show that this concept ensures local conditioning in the nonconvex case via an abstract subdifferential; in the convex case, we obtain complete characterizations of global conditioning in terms of an extension of the upper-Lipschitz property.

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Authors and Affiliations

  1. Departamento de Ingenieria de Sistemas, Aplicada, Universidad de Talca, Curicó, Chile

    O. Cornejo (Assistant Professor)

  2. Analyse Appliquée et Optimisation, Université de Bourgogne, Dijon, France

    A. Jourani (Professor)

  3. Faculty of Mathematics, University Al. I. Cuza, Iaşi, Romania

    C. Zălinescu (Professor)

Authors
  1. O. Cornejo
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  2. A. Jourani
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  3. C. Zălinescu
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Cornejo, O., Jourani, A. & Zălinescu, C. Conditioning and Upper-Lipschitz Inverse Subdifferentials in Nonsmooth Optimization Problems. Journal of Optimization Theory and Applications 95, 127–148 (1997). https://doi.org/10.1023/A:1022687412779

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  • DOI: https://doi.org/10.1023/A:1022687412779

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