Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm

Guo, Yongfeng; Cui, Wei

doi:10.1186/s13660-018-1695-x

Cited by 14 publications

(20 citation statements)

References 30 publications

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“…Bounded perturbation resilience with respect to a nonempty solution set, recall Definition 2.3, is known to hold for the basic Landweber and projected Landweber iteration, see [42,34] and Table 1. This implies bounded perturbation resilience of A LW and A LW + .…”

Section: Perturbationmentioning

confidence: 99%

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

2020

J. Appl. Numer. Optim.

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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.

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Section: Perturbationmentioning

confidence: 99%

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

2020

J. Appl. Numer. Optim.

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“…For the state of current research on superiorization one can check the website [7]. In particular, see [9,13,14,15,20] for some recent papers on superiorization in the context of least squares minimization including (1.2).…”

Section: )mentioning

confidence: 99%

Superiorized regularization of inverse problems

2020

J. Appl. Numer. Optim.

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Inverse problems are characterized by their inherent non-uniqueness and sensitivity with respect to data perturbations. Their stable solution requires the application of regularization methods including variational and iterative regularization methods. Superiorization is a heuristic approach that can steer basic iterative algorithms to have small value of a certain regularization functional while keeping the algorithms simplicity and computational efforts, and is able to account for additional prior information. In this note, we combine the superiorization methodology with iterative regularization and show that the superiorized version of the scheme yields again a regularization method, however accounting for different prior information.

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“…On the other hand, the bounded perturbation resilience and superiorization of iterative methods are extensively studied in many references, for example, [3,9,16,18,20,29]. The problem has received much attention due to its applications in convex feasibility problems [10], image reconstruction [15] and inverse problems of radiation therapy [14], and so on.…”

Section: Introductionmentioning

confidence: 99%

“…He established weak convergence of the above algorithm in [29] under appropriate conditions imposed on {τ n }, and {γ n }. Very recently, Guo and Cui [18] introduced a modified proximal gradient algorithm with bounded perturbations. Indeed, their iterative sequence {x n } is generated as follows…”

Section: Introductionmentioning

confidence: 99%

Bounded perturbation resilience of generalized viscosity iterative algorithms for split variational inclusion problems

2020

Appl. Set-Valued Anal. Optim.

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In this paper, we propose a generalized viscosity approximation method combing a sequence of contractive mappings to solve a split variational inclusion problem. The bounded perturbation resilience of the method is investigated in Hilbert spaces. Under mild conditions, we prove that our algorithms strongly converge to a solution of the split variational inclusion problem, which is also the unique solution of some variational inequality problem. Furthermore, we show the convergence and effectiveness of the algorithms via two numerical examples. Our results extend and improve the related results in the literature.

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Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm

Cited by 14 publications

References 30 publications

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

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

Superiorized regularization of inverse problems

Bounded perturbation resilience of generalized viscosity iterative algorithms for split variational inclusion problems

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