Superiorization vs. accelerated convex optimization: The superiorized / regularized least-squares case

Yair Censor, Stefania Petra, Christoph Schnörr

Research output: Contribution to journalArticlepeer-review

Abstract

We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized / regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds. Regarding superiorization, the state of the art is examined for this problem class, and a novel approach is proposed that employs proximal mappings and is structurally similar to the established forward-backward optimization approach. Regarding convex optimization, accelerated forward-backward splitting with inexact proximal maps is worked out and applied to both the natural splitting least-squares term / regularizer and to the reverse splitting regularizer / least-squares term. Our numerical findings suggest that superiorization can approach the solution of the optimization problem and leads to comparable results at significantly lower costs, after appropriate parameter tuning. On the other hand, applying accelerated forward-backward optimization to the reverse splitting slightly outperforms superiorization, which suggests that convex optimization can approach superiorization too, using a suitable problem splitting.

Original languageEnglish
Pages (from-to)15-62
Number of pages48
JournalJournal of Applied and Numerical Optimization
Volume2
Issue number1
DOIs
StatePublished - Apr 2020

Bibliographical note

Publisher Copyright:
© 2020 Journal of Applied and Numerical Optimization.

Keywords

  • Accelerated forward-backward iteration
  • Convex optimization
  • Inexact proximal mappings
  • Perturbation resilience
  • Superiorization

ASJC Scopus subject areas

  • Computational Mathematics
  • Control and Optimization
  • Numerical Analysis
  • Modeling and Simulation

Fingerprint

Dive into the research topics of 'Superiorization vs. accelerated convex optimization: The superiorized / regularized least-squares case'. Together they form a unique fingerprint.

Cite this