Derivative-free superiorization with component-wise perturbations

Yair Censor, Howard Heaton, Reinhard Schulte

Research output: Contribution to journalArticlepeer-review


Superiorization reduces, not necessarily minimizes, the value of a target function while seeking constraints compatibility. This is done by taking a solely feasibility-seeking algorithm, analyzing its perturbation resilience, and proactively perturbing its iterates accordingly to steer them toward a feasible point with reduced value of the target function. When the perturbation steps are computationally efficient, this enables generation of a superior result with essentially the same computational cost as that of the original feasibility-seeking algorithm. In this work, we refine previous formulations of the superiorization method to create a more general framework, enabling target function reduction steps that do not require partial derivatives of the target function. In perturbations that use partial derivatives, the step-sizes in the perturbation phase of the superiorization method are chosen independently from the choice of the nonascent directions. This is no longer true when component-wise perturbations are employed. In that case, the step-sizes must be linked to the choice of the nonascent direction in every step. Besides presenting and validating these notions, we give a computational demonstration of superiorization with component-wise perturbations for a problem of computerized tomography image reconstruction.

Original languageEnglish
Pages (from-to)1219-1240
Number of pages22
JournalNumerical Algorithms
Issue number4
StatePublished - 4 Apr 2019

Bibliographical note

Funding Information:
This project was supported by Research Grant No. 2013003 of the United States-Israel Binational Science Foundation (BSF) and by Award No. 1P20183640-01A1 of the National Cancer Institute (NCI) of the National Institutes of Health (NIH).

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.


  • Component-wise perturbations
  • Derivative-free
  • Feasibility-seeking
  • Image reconstruction
  • Perturbation resilience
  • Superiorization

ASJC Scopus subject areas

  • Applied Mathematics


Dive into the research topics of 'Derivative-free superiorization with component-wise perturbations'. Together they form a unique fingerprint.

Cite this