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General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems

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  • Zhongming Wu

    (Southeast University)

  • Min Li

    (Nanjing University)

Abstract

In this paper, we consider a general inertial proximal gradient method with constant and variable stepsizes for a class of nonconvex nonsmooth optimization problems. The proposed method incorporates two different extrapolations with respect to the previous iterates into the backward proximal step and the forward gradient step in classic proximal gradient method. Under more general parameter constraints, we prove that the proposed method generates a convergent subsequence and each limit point is a stationary point of the problem. Furthermore, the generated sequence is globally convergent to a stationary point if the objective function satisfies the Kurdyka–Łojasiewicz property. Local linear convergence also can be established for the proposed method with constant stepsizes by using a common error bound condition. In addition, we conduct some numerical experiments on nonconvex quadratic programming and SCAD penalty problems to demonstrate the advantage of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:73:y:2019:i:1:d:10.1007_s10589-019-00073-1
    DOI: 10.1007/s10589-019-00073-1
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    Cited by:

    1. Xiaoqi Yang & Chenchen Zu, 2022. "Convergence of Inexact Quasisubgradient Methods with Extrapolation," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 676-703, June.
    2. Zhongming Wu & Chongshou Li & Min Li & Andrew Lim, 2021. "Inertial proximal gradient methods with Bregman regularization for a class of nonconvex optimization problems," Journal of Global Optimization, Springer, vol. 79(3), pages 617-644, March.
    3. Zhili Ge & Zhongming Wu & Xin Zhang & Qin Ni, 2023. "An extrapolated proximal iteratively reweighted method for nonconvex composite optimization problems," Journal of Global Optimization, Springer, vol. 86(4), pages 821-844, August.
    4. Szilárd Csaba László, 2023. "A Forward–Backward Algorithm With Different Inertial Terms for Structured Non-Convex Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 387-427, July.
    5. Lulu He & Jimin Ye & E. Jianwei, 2023. "Accelerated Stochastic Variance Reduction for a Class of Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 810-828, March.
    6. Min Li & Zhongming Wu, 2019. "Convergence Analysis of the Generalized Splitting Methods for a Class of Nonconvex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 535-565, November.

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