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Calculus Rules of the Generalized Concave Kurdyka–Łojasiewicz Property

Author

Listed:
  • Xianfu Wang

    (University of British Columbia)

  • Ziyuan Wang

    (University of British Columbia)

Abstract

In this paper, we propose several calculus rules for the generalized concave Kurdyka–Łojasiewicz (KL) property, which generalize Li and Pong’s results for KL exponents. The optimal concave desingularizing function has various forms and may be nondifferentiable. Our calculus rules do not assume desingularizing functions to have any specific form nor differentiable, while the known results do. Several examples are also given to show that our calculus rules are applicable to a broader class of functions than the known ones.

Suggested Citation

  • Xianfu Wang & Ziyuan Wang, 2023. "Calculus Rules of the Generalized Concave Kurdyka–Łojasiewicz Property," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 839-854, June.
  • Handle: RePEc:spr:joptap:v:197:y:2023:i:3:d:10.1007_s10957-023-02219-y
    DOI: 10.1007/s10957-023-02219-y
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    References listed on IDEAS

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    1. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
    2. Yuqia Wu & Shaohua Pan & Shujun Bi, 2021. "Kurdyka–Łojasiewicz Property of Zero-Norm Composite Functions," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 94-112, January.
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