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Some accelerated alternating proximal gradient algorithms for a class of nonconvex nonsmooth problems

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  • Xin Yang

    (Zhejiang University)

  • Lingling Xu

    (Nanjing Normal University)

Abstract

In this paper, we study a class of nonconvex and nonsmooth optimization problems, whose objective function can be split into two separable terms and one coupling term. Alternating proximal gradient methods combining with extrapolation are proposed to solve such problems. Under some assumptions, we prove that every cluster point of the sequence generated by our algorithms is a critical point. Furthermore, if the objective function satisfies Kurdyka–Łojasiewicz property, the generated sequence is globally convergent to a critical point. In order to make the algorithm more effective and flexible, we also use some strategies to update the extrapolation parameter and solve the problems with unknown Lipschitz constant. Numerical experiments demonstrate the effectiveness of our algorithms.

Suggested Citation

  • Xin Yang & Lingling Xu, 2023. "Some accelerated alternating proximal gradient algorithms for a class of nonconvex nonsmooth problems," Journal of Global Optimization, Springer, vol. 87(2), pages 939-964, November.
    • Handle: RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01214-3
    DOI: 10.1007/s10898-022-01214-3
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    References listed on IDEAS

    as
    1. Zhongming Wu & Min Li, 2019. "General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 73(1), pages 129-158, May.
    2. Yurii Nesterov, 2018. "Lectures on Convex Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-91578-4, December.
    3. Xue Gao & Xingju Cai & Deren Han, 2020. "A Gauss–Seidel type inertial proximal alternating linearized minimization for a class of nonconvex optimization problems," Journal of Global Optimization, Springer, vol. 76(4), pages 863-887, April.
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