Can linear superiorization be useful for linear optimization problems?

Censor, Yair

doi:10.1088/1361-6420/33/4/044006

Cited by 22 publications

(29 citation statements)

References 35 publications

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“…The NTVS algorithm investigated in this work combines properties that were scattered among previous works on TVS in x-ray CT, see the Appendix of [28]. These properties, listed next, were never combined in a single algorithm, as we do here, neither for x-ray CT nor for pCT.…”

Section: B Ntvs Algorithmmentioning

confidence: 99%

An Improved Method of Total Variation Superiorization Applied to Reconstruction in Proton Computed Tomography

Schultze

Censor

Karbasi

et al. 2020

IEEE Trans. Med. Imaging

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NOTE: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.Abstract-Previous work has shown that total variation superiorization (TVS) improves reconstructed image quality in proton computed tomography (pCT). The structure of the TVS algorithm has evolved since then and this work investigated if this new algorithmic structure provides additional benefits to pCT image quality. Structural and parametric changes introduced to the original TVS algorithm included: (1) inclusion or exclusion of TV reduction requirement, (2) a variable number, N , of TV perturbation steps per feasibility-seeking iteration, and (3) introduction of a perturbation kernel 0 < α < 1. The structural change of excluding the TV reduction requirement check tended to have a beneficial effect for 3 ≤ N ≤ 6 and allows full parallelization of the TVS algorithm. Repeated perturbations per feasibility-seeking iterations reduced total variation (TV) and material dependent standard deviations for 3 ≤ N ≤ 6. The perturbation kernel α, equivalent to α = 0.5 in the original TVS algorithm, reduced TV and standard deviations as α was increased beyond α = 0.5, but negatively impacted reconstructed relative stopping power (RSP) values for α > 0.75. The reductions in TV and standard deviations allowed feasibilityseeking with a larger relaxation parameter λ than previously used, without the corresponding increases in standard deviations experienced with the original TVS algorithm. This work demonstrates that the modifications related to the evolution of the original TVS algorithm provide benefits in terms of both pCT image quality and computational efficiency for appropriately chosen parameter values.

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Section: B Ntvs Algorithmmentioning

confidence: 99%

An Improved Method of Total Variation Superiorization Applied to Reconstruction in Proton Computed Tomography

Schultze

Censor

Karbasi

et al. 2020

IEEE Trans. Med. Imaging

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“…Some of the results in [5] are based on earlier results of Butnariu, Reich and Zaslavski [6,7,8]. For the state of current research on superiorization, visit the webpage: "Superiorization and Perturbation Resilience of Algorithms: A Bibliography compiled and continuously updated by Yair Censor" at: http://math.haifa.ac.il/yair/bib-superiorization-censor.html and in particular see [12,Section 3] and [10,Appendix].…”

Section: Bounded Perturbation Resiliencementioning

confidence: 99%

Convergence of projection and contraction algorithms with outer perturbations and their applications to sparse signals recovery

Dong

Gibali

Jiang

et al. 2018

J. Fixed Point Theory Appl.

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In this paper we study the bounded perturbation resilience of projection and contraction algorithms for solving variational inequality (VI) problems in real Hilbert spaces. Under typical and standard assumptions of monotonicity and Lipschitz continuity of the VI's associated mapping, convergence of the perturbed projection and contraction algorithms is proved. Based on the bounded perturbed resilience of projection and contraction algorithms, we present some inertial projection and contraction algorithms. In addition we show that the perturbed algorithms converges at the rate of O(1/t).Mathematics Subject Classification (2010). Primary 49J35, 58E35; Secondary 65K15, 90C47.

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“…that any sequence (x ′ n ) n , generated by this process, converges to some point x ′ ∞ ∈ C. An algorithm that employs such a process is called a 'superiorized version of the basic algorithm'. Modifications of this superiorized version of the basic algorithm have been developed, see, e.g., the Appendix, entitled: "The algorithmic evolution of superiorization" in [12], however, our current investigation focuses solely on the above formulation.…”

Section: Introductionmentioning

confidence: 99%

An Analysis of the Superiorization Method via the Principle of Concentration of Measure

Censor

Levy

2019

Appl Math Optim

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The superiorization methodology is intended to work with input data of constrained minimization problems, i.e., a target function and a constraints set. However, it is based on an antipodal way of thinking to the thinking that leads constrained minimization methods. Instead of adapting unconstrained minimization algorithms to handling constraints, it adapts feasibility-seeking algorithms to reduce (not necessarily minimize) target function values. This is done while retaining the feasibility-seeking nature of the algorithm and without paying a high computational price. A guarantee that the local target function * Corresponding author.

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Can linear superiorization be useful for linear optimization problems?

Cited by 22 publications

References 35 publications

An Improved Method of Total Variation Superiorization Applied to Reconstruction in Proton Computed Tomography

An Improved Method of Total Variation Superiorization Applied to Reconstruction in Proton Computed Tomography

Convergence of projection and contraction algorithms with outer perturbations and their applications to sparse signals recovery

An Analysis of the Superiorization Method via the Principle of Concentration of Measure

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