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Kurdyka–Łojasiewicz Property of Zero-Norm Composite Functions

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  • Yuqia Wu

    (South China University of Technology)

  • Shaohua Pan

    (South China University of Technology)

  • Shujun Bi

    (South China University of Technology)

Abstract

This paper focuses on a class of zero-norm composite optimization problems. For this class of nonconvex nonsmooth problems, we establish the Kurdyka–Łojasiewicz property of exponent being a half for its objective function under a suitable assumption and provide some examples to illustrate that such an assumption is not very restricted which, in particular, involve the zero-norm regularized or constrained piecewise linear–quadratic function, the zero-norm regularized or constrained logistic regression function, the zero-norm regularized or constrained quadratic function over a sphere.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:188:y:2021:i:1:d:10.1007_s10957-020-01779-7
    DOI: 10.1007/s10957-020-01779-7
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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. P. Tseng & S. Yun, 2009. "Block-Coordinate Gradient Descent Method for Linearly Constrained Nonsmooth Separable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 513-535, March.
    3. JOURNEE, Michel & NESTEROV, Yurii & RICHTARIK, Peter & SEPULCHRE, Rodolphe, 2010. "Generalized power method for sparse principal component analysis," LIDAM Reprints CORE 2232, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. 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.

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