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Inertial proximal gradient methods with Bregman regularization for a class of nonconvex optimization problems

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  • Zhongming Wu

    (Nanjing University of Information Science and Technology)

  • Chongshou Li

    (National University of Singapore)

  • Min Li

    (Nanjing University)

  • Andrew Lim

    (National University of Singapore)

Abstract

This paper proposes an inertial Bregman proximal gradient method for minimizing the sum of two possibly nonconvex functions. This method includes two different inertial steps and adopts the Bregman regularization in solving the subproblem. Under some general parameter constraints, we prove the subsequential convergence that each generated sequence converges to the stationary point of the considered problem. To overcome the parameter constraints, we further propose a nonmonotone line search strategy to make the parameter selections more flexible. The subsequential convergence of the proposed method with line search is established. When the line search is monotone, we prove the stronger global convergence and linear convergence rate under Kurdyka–Łojasiewicz framework. Moreover, numerical results on SCAD and MCP nonconvex penalty problems are reported to demonstrate the effectiveness and superiority of the proposed methods and line search strategy.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:79:y:2021:i:3:d:10.1007_s10898-020-00943-7
    DOI: 10.1007/s10898-020-00943-7
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    Cited by:

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    2. 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.
    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.

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