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The Exact Modulus of the Generalized Concave Kurdyka-Łojasiewicz Property

Author

Listed:
  • Xianfu Wang

    (Department of Mathematics, University of British Columbia, Kelowna, British Columbia V1V 1V7, Canada)

  • Ziyuan Wang

    (Department of Mathematics, University of British Columbia, Kelowna, British Columbia V1V 1V7, Canada)

Abstract

We introduce a generalized version of the concave Kurdyka-Łojasiewicz (KL) property by employing nonsmooth desingularizing functions. We also present the exact modulus of the generalized concave KL property, which provides an answer to the open question regarding the optimal concave desingularizing function. The exact modulus is designed to be the smallest among all possible concave desingularizing functions. Examples are given to illustrate this pleasant property. In turn, using the exact modulus, we provide the sharpest upper bound for the total length of iterates generated by the celebrated Bolte-Sabach-Teboulle proximal alternating linearized minimization algorithm.

Suggested Citation

  • Xianfu Wang & Ziyuan Wang, 2022. "The Exact Modulus of the Generalized Concave Kurdyka-Łojasiewicz Property," Mathematics of Operations Research, INFORMS, vol. 47(4), pages 2765-2783, November.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:4:p:2765-2783
    DOI: 10.1287/moor.2021.1227
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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. Bo Wen & Xiaojun Chen & Ting Kei Pong, 2018. "A proximal difference-of-convex algorithm with extrapolation," Computational Optimization and Applications, Springer, vol. 69(2), pages 297-324, March.
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    Cited by:

    1. Xianfu Wang & Ziyuan Wang, 2024. "A Bregman inertial forward-reflected-backward method for nonconvex minimization," Journal of Global Optimization, Springer, vol. 89(2), pages 327-354, June.

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