EURO Journal on Computational Optimization

, Volume 4, Issue 1, pp 3–25 | Cite as

An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions

  • Radu Ioan BoţEmail author
  • Ernö Robert Csetnek
  • Szilárd Csaba László
Original Paper


We propose a forward–backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. Every sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-Łojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. We illustrate the theoretical results by considering two numerical experiments: the first one concerns the ability of recovering the local optimal solutions of nonconvex optimization problems, while the second one refers to the restoration of a noisy blurred image.


Nonsmooth optimization Limiting subdifferential Kurdyka-Łojasiewicz inequality Bregman distance Inertial proximal algorithm 

Mathematics subject classification

90C26 90C30 65K10 



The authors are thankful to two anonymous reviewers for pertinent comments and remarks which improved the quality of the paper.


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Copyright information

© EURO - The Association of European Operational Research Societies 2015

Authors and Affiliations

  • Radu Ioan Boţ
    • 1
    Email author
  • Ernö Robert Csetnek
    • 1
  • Szilárd Csaba László
    • 2
  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Department of MathematicsTechnical University of Cluj-NapocaCluj-NapocaRomania

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