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Fast inertial dynamic algorithm with smoothing method for nonsmooth convex optimization

Author

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  • Xin Qu

    (Harbin Institute of Technology, School of Mathematics)

  • Wei Bian

    (Harbin Institute of Technology, School of Mathematics)

Abstract

In order to solve the minimization of a nonsmooth convex function, we design an inertial second-order dynamic algorithm, which is obtained by approximating the nonsmooth function by a class of smooth functions. By studying the asymptotic behavior of the dynamic algorithm, we prove that each trajectory of it weakly converges to an optimal solution under some appropriate conditions on the smoothing parameters, and the convergence rate of the objective function values is $$o\left( t^{-2}\right)$$ o t - 2 . We also show that the algorithm is stable, that is, this dynamic algorithm with a perturbation term owns the same convergence properties when the perturbation term satisfies certain conditions. Finally, we verify the theoretical results by some numerical experiments.

Suggested Citation

  • Xin Qu & Wei Bian, 2022. "Fast inertial dynamic algorithm with smoothing method for nonsmooth convex optimization," Computational Optimization and Applications, Springer, vol. 83(1), pages 287-317, September.
    • Handle: RePEc:spr:coopap:v:83:y:2022:i:1:d:10.1007_s10589-022-00388-6
    DOI: 10.1007/s10589-022-00388-6
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    References listed on IDEAS

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    1. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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