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Bundle Method for Non-Convex Minimization with Inexact Subgradients and Function Values

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Computational and Analytical Mathematics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 50))

Abstract

We discuss a bundle method to minimize locally Lipschitz functions which are both nonconvex and nonsmooth. We analyze situations where only inexact subgradients or function values are available. For suitable classes of such non-smooth functions we prove convergence of our algorithm to approximate critical points.

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Notes

  1. 1.

    Communicated by Heinz H. Bauschke.

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Acknowledgements

The author acknowledges funding by Fondation d’Entreprise EADS under grant Technicom and by Fondation de Recherche pour l’Aéronautique et l’Espace under grant Survol.

Author information

Authors and Affiliations

  1. Institut de Mathématiques, Université Paul Sabatier, Toulouse, France

    Dominikus Noll

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  1. Dominikus Noll
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Correspondence to Dominikus Noll .

Editor information

Editors and Affiliations

  1. Lawrence Berkeley National Laboratory, Berkeley, USA

    David H. Bailey

  2. Mathematics, University of British Columbia, Kelowna, British Columbia, Canada

    Heinz H. Bauschke

  3. Dept. Mathematics & Statistics, Simon Fraser University, Burnaby, British Columbia, Canada

    Peter Borwein

  4. Mathematics, University of Florida, Gainesville, Florida, USA

    Frank Garvan

  5. Mathematics and Computer Science, University of Limoges, Limoges, France

    Michel Théra

  6. Mathematics and Computer Science Department, La Sierra University, Riverside, California, USA

    Jon D. Vanderwerff

  7. Dept. Combinatorics & Optimization, University of Waterloo Faculty of Mathematics, Waterloo, Ontario, Canada

    Henry Wolkowicz

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Communicated By Heinz H. Bauschke.

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Noll, D. (2013). Bundle Method for Non-Convex Minimization with Inexact Subgradients and Function Values. In: Bailey, D., et al. Computational and Analytical Mathematics. Springer Proceedings in Mathematics & Statistics, vol 50. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7621-4_26

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