A gradient-type algorithm with backward inertial steps associated to a nonconvex minimization problem

  • Cristian Daniel Alecsa
  • Szilárd Csaba LászlóEmail author
  • Adrian Viorel
Original Paper


We investigate an algorithm of gradient type with a backward inertial step in connection with the minimization of a nonconvex differentiable function. We show that the generated sequences converge to a critical point of the objective function, if a regularization of the objective function satisfies the Kurdyka-Łojasiewicz property. Further, we provide convergence rates for the generated sequences and the objective function values formulated in terms of the Łojasiewicz exponent. Finally, some numerical experiments are presented in order to compare our numerical scheme with some algorithms well known in the literature.


Inertial algorithm Nonconvex optimization Kurdyka-Łojasiewicz inequality Convergence rate 

Mathematics Subject Classification (2010)

90C26 90C30 65K10 



The authors are thankful to three anonymous reviewers for remarks and suggestions which helped us to improve the quality of the paper.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Tiberiu Popoviciu Institute of Numerical AnalysisRomanian AcademyCluj-NapocaRomania
  2. 2.Department of MathematicsBabes-Bolyai UniversityCluj-NapocaRomania
  3. 3.Department of MathematicsTechnical University of Cluj-NapocaCluj-NapocaRomania

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