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Application of Consistent Massage-Like Perturbations on Mouse Calves and Monitoring the Resulting Intramuscular Pressure Changes
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Derivative-free superiorization with component-wise perturbations.

Yair Censor1, Howard Heaton2, Reinhard Schulte3

  • 1Department of Mathematics, University of Haifa, Mt. Carmel, 3498838, Haifa, Israel.

Numerical Algorithms
|May 10, 2019
PubMed
Summary
This summary is machine-generated.

Superiorization is a method that improves results by adjusting algorithms to meet constraints while reducing a target function. This refined approach enhances feasibility-seeking algorithms without increasing computational cost.

Keywords:
Component-wise perturbationsDerivative-freeFeasibility-seekingImage reconstructionPerturbation resilienceSuperiorization

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Area of Science:

  • Optimization Algorithms
  • Computational Mathematics
  • Image Reconstruction

Background:

  • Superiorization method aims to reduce a target function's value while satisfying constraints.
  • Existing methods often rely on partial derivatives and independent step-size choices.
  • Computational efficiency is key for practical application of superiorization.

Purpose of the Study:

  • To refine the superiorization method into a more general framework.
  • To enable target function reduction without requiring partial derivatives.
  • To explore component-wise perturbations and their impact on step-size selection.

Main Methods:

  • Developed a generalized superiorization framework.
  • Introduced component-wise perturbations, linking step-sizes to nonascent directions.
  • Validated the refined method computationally on computerized tomography image reconstruction.

Main Results:

  • Demonstrated a generalized superiorization approach applicable without partial derivatives.
  • Showcased the necessity of linking step-sizes to nonascent directions in component-wise perturbations.
  • Achieved superior results in image reconstruction with comparable computational cost.

Conclusions:

  • The refined superiorization method offers a more flexible and general approach to optimization.
  • Component-wise perturbations require careful consideration of step-size and direction interdependence.
  • The method shows promise for applications like medical image reconstruction.