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Fast inertial dynamic algorithm with smoothing method for nonsmooth convex optimization

Xin Qu () and Wei Bian ()
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Xin Qu: Harbin Institute of Technology, School of Mathematics
Wei Bian: Harbin Institute of Technology, School of Mathematics

Computational Optimization and Applications, 2022, vol. 83, issue 1, No 9, 287-317

Abstract: 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.

Keywords: Nonsmooth optimization; Smoothing method; Convex minimization; Convergence rate; 90C25; 90C30; 65K05; 37N40 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-022-00388-6

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