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.
|Number of pages||48|
|Journal||Journal of Applied and Numerical Optimization|
|State||Published - Apr 2020|
Bibliographical noteFunding Information:
We are grateful to the three anonymous reviewers for their constructive comments that helped us improve the paper. The work of the YC was supported by the ISF-NSFC joint research program grant No. 2874/19.
© 2020 Journal of Applied and Numerical Optimization.
- Accelerated forward-backward iteration
- Convex optimization
- Inexact proximal mappings
- Perturbation resilience
ASJC Scopus subject areas
- Computational Mathematics
- Control and Optimization
- Modeling and Simulation
- Numerical Analysis