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

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Abstract

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.

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Acknowledgments

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. Department of Mathematics, University of Kurdistan, Sanandaj, Iran

    Mohsen Hoseini & Shahram Saeidi

  2. Department of Applied Mathematics, Pukyong National University, Busan, 48513, Republic of Korea

    Do Sang Kim

Authors
  1. Mohsen Hoseini
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  2. Shahram Saeidi
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  3. Do Sang Kim
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Correspondence to Mohsen Hoseini.

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Hoseini, M., Saeidi, S. & Kim, D.S. On perturbed hybrid steepest descent method with minimization or superiorization for subdifferentiable functions. Numer Algor 85, 353–374 (2020). https://doi.org/10.1007/s11075-019-00818-3

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