On perturbed hybrid steepest descent method with minimization or superiorization for subdifferentiable functions

  • Mohsen HoseiniEmail author
  • Shahram Saeidi
  • Do Sang Kim
Original Paper


For finding the minimum value of differentiable functions over a nonempty closed convex subset of a Hilbert space, the hybrid steepest descent method (HSDM) can be applied. In this work, we study perturbed algorithms in line with a generalized HSDM and discuss how some selections of perturbations enable us to increase the convergence speed. When we specialize these results to constrained minimization then the perturbations become bounded perturbations used in the superiorization methodology (SM). We show usefulness of the SM in studying the constrained convex minimization problem for subdifferentiable functions and proceed with the study of the computational efficiency of the SM compared with the HSDM. In the computational experiment comparing the HSDM with superiorization, the latter seems to be advantageous for the specific experiment.


Variational inequality Perturbation Superiorization Hybrid steepest descent method 



The authors would like to thank the referee for giving valuable and constructive comments that greatly contributed to improving the final version of this paper.


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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KurdistanSanandajIran
  2. 2.Department of Applied MathematicsPukyong National UniversityBusanRepublic of Korea

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