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Conditioning and Upper-Lipschitz Inverse Subdifferentials in Nonsmooth Optimization Problems

Author

Listed:
  • O. Cornejo

    (Universidad de Talca)

  • A. Jourani

    (Université de Bourgogne)

  • C. Zălinescu

    (University Al. I. Cuza)

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.

Suggested Citation

  • O. Cornejo & A. Jourani & C. Zălinescu, 1997. "Conditioning and Upper-Lipschitz Inverse Subdifferentials in Nonsmooth Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 127-148, October.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:1:d:10.1023_a:1022687412779
    DOI: 10.1023/A:1022687412779
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    References listed on IDEAS

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    1. Correa Romar, 2014. "Mathematical Foci," Mathematical Economics Letters, De Gruyter, vol. 2(1-2), pages 5-11, August.
    2. Stephen M. Robinson, 1976. "Regularity and Stability for Convex Multivalued Functions," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 130-143, May.
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    Cited by:

    1. Alexander Y. Kruger, 2016. "Nonlinear Metric Subregularity," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 820-855, December.
    2. Radu Boţ & Ernö Csetnek, 2012. "Error bound results for convex inequality systems via conjugate duality," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 296-309, July.
    3. A. Jourani & D. Zagrodny, 2012. "The positiveness of lower limits of the Hoffman constant in parametric polyhedral programs," Journal of Global Optimization, Springer, vol. 53(4), pages 641-661, August.
    4. C. Zălinescu, 2003. "A Nonlinear Extension of Hoffman's Error Bounds for Linear Inequalities," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 524-532, August.

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