Superiorization and Perturbation Resilience of Algorithms: A Continuously Updated Bibliography

This document presents a, (mostly) chronologically ordered, bibliography of scientific publications on the superiorization methodology and perturbation resilience of algorithms which is compiled and continuously updated by us at: http://math.haifa.ac.il/yair/bib-superiorization-censor.html. Since the beginings of this topic we try to trace the work that has been published about it since its inception. To the best of our knowledge this bibliography represents all available publications on this topic to date, and while the URL is continuously updated we will revise this document and bring it up to date on arXiv approximately once a year. Abstracts of the cited works, and some links and downloadable files of preprints or reprints are available on the above mentioned Internet page. If you know of a related scientific work in any form that should be included here kindly write to me on: [email protected] with full bibliographic details, a DOI if available, and a PDF copy of the work if possible. The Internet page was initiated on March 7, 2015, and has been last updated on March 12, 2020.Comment: Original report: June 13, 2015 contained 41 items. First revision: March 9, 2017 contained 64 items. Second revision: March 8, 2018 contained 76 items. Third revision: March 11, 2019 contains 90 items. Fourth revision: March 16, 2020 contains 112 item

A Heuristic Superiorization-Like Approach to Bioluminescence Tomography

Bioluminescence tomography (BLT) is a powerful molecular imaging technology designed for the localization and quantification of bioluminescent sources in vivo. With the forward process modeled by the diffusion approximation equation, BLT is the inverse problem to reconstruct the distribution of internal bioluminescent sources subject to Cauchy data. Due to the non-uniqueness of BLT in general, adequate prior information such as nonnegativity and source support constraints must be utilized to obtain a physically favorable BLT solution. Iterative algorithms such as the well-known Expectation Maximization (EM) algorithm and the Landweber algorithm which are suitable for incorporating these knowledge-based constraints are widely used in practice. In the current work, we investigate the application of a superiorization-like approach to BLT. A superiorization-like version of prototypical iterative algorithms for BLT in a general framework, denoted by S-BLT, is presented. For the EM algorithm as the underlying iterative algorithms for BLT and S-BLT, superiorized by the total variation (TV) merit function, preliminary simulation results for a heterogeneous phantom are reported to demonstrate the viability of the approach and evaluate the performance of the proposed algorithm. It is found that total variation superiorization of BLT can significantly improve the visualization effect of the reconstruction with the sources set as a particular case of radial basis functions. ? 2013 Springer-Verlag.EI

Bounded perturbation resilience of projected scaled gradient methods

We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected Newton method, the projected Landweber-type methods and the generalized Expectation-Maximization (EM)-type methods. We prove the convergence of the PSG methods in the presence of bounded perturbations. This resilience to bounded perturbations is relevant to the ability to apply the recently developed superiorization methodology to PSG methods, in particular to the EM algorithm.Comment: Computational Optimization and Applications, accepted for publicatio

Accelerating two projection methods via perturbations with application to Intensity-Modulated Radiation Therapy

Constrained convex optimization problems arise naturally in many real-world applications. One strategy to solve them in an approximate way is to translate them into a sequence of convex feasibility problems via the recently developed level set scheme and then solve each feasibility problem using projection methods. However, if the problem is ill-conditioned, projection methods often show zigzagging behavior and therefore converge slowly. To address this issue, we exploit the bounded perturbation resilience of the projection methods and introduce two new perturbations which avoid zigzagging behavior. The first perturbation is in the spirit of $k$-step methods and uses gradient information from previous iterates. The second uses the approach of surrogate constraint methods combined with relaxed, averaged projections. We apply two different projection methods in the unperturbed version, as well as the two perturbed versions, to linear feasibility problems along with nonlinear optimization problems arising from intensity-modulated radiation therapy (IMRT) treatment planning. We demonstrate that for all the considered problems the perturbations can significantly accelerate the convergence of the projection methods and hence the overall procedure of the level set scheme. For the IMRT optimization problems the perturbed projection methods found an approximate solution up to 4 times faster than the unperturbed methods while at the same time achieving objective function values which were 0.5 to 5.1% lower.Comment: Accepted for publication in Applied Mathematics & Optimizatio