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An Inertial Tseng’s Type Proximal Algorithm for Nonsmooth and Nonconvex Optimization Problems

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Abstract

We investigate the convergence of a forward–backward–forward proximal-type algorithm with inertial and memory effects when minimizing the sum of a nonsmooth function with a smooth one in the absence of convexity. The convergence is obtained provided an appropriate regularization of the objective satisfies the Kurdyka–Łojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Radu Ioan Boţ & Ernö Robert Csetnek

Authors
  1. Radu Ioan Boţ
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  2. Ernö Robert Csetnek
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Correspondence to Radu Ioan Boţ.

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Research partially supported by DFG (German Research Foundation), project BO 2516/4-1.

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Boţ, R.I., Csetnek, E.R. An Inertial Tseng’s Type Proximal Algorithm for Nonsmooth and Nonconvex Optimization Problems. J Optim Theory Appl 171, 600–616 (2016). https://doi.org/10.1007/s10957-015-0730-z

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  • DOI: https://doi.org/10.1007/s10957-015-0730-z

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