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Bounded Perturbation Resilience and Superiorization of Proximal Scaled Gradient Algorithm with Multi-Parameters

Author

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  • Yanni Guo

    (College of Science, Civil Aviation University of China, Tianjin 300300, China)

  • Xiaozhi Zhao

    (College of Science, Civil Aviation University of China, Tianjin 300300, China)

Abstract

In this paper, a multi-parameter proximal scaled gradient algorithm with outer perturbations is presented in real Hilbert space. The strong convergence of the generated sequence is proved. The bounded perturbation resilience and the superiorized version of the original algorithm are also discussed. The validity and the comparison with the use or not of superiorization of the proposed algorithms were illustrated by solving the l 1 − l 2 problem.

Suggested Citation

  • Yanni Guo & Xiaozhi Zhao, 2019. "Bounded Perturbation Resilience and Superiorization of Proximal Scaled Gradient Algorithm with Multi-Parameters," Mathematics, MDPI, vol. 7(6), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:535-:d:239111
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    References listed on IDEAS

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    1. Yair Censor & Ran Davidi & Gabor T. Herman & Reinhard W. Schulte & Luba Tetruashvili, 2014. "Projected Subgradient Minimization Versus Superiorization," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 730-747, March.
    2. Wenma Jin & Yair Censor & Ming Jiang, 2016. "Bounded perturbation resilience of projected scaled gradient methods," Computational Optimization and Applications, Springer, vol. 63(2), pages 365-392, March.
    3. Yair Censor & Alexander Zaslavski, 2013. "Convergence and perturbation resilience of dynamic string-averaging projection methods," Computational Optimization and Applications, Springer, vol. 54(1), pages 65-76, January.
    4. Yair Censor & Wei Chen & Patrick Combettes & Ran Davidi & Gabor Herman, 2012. "On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints," Computational Optimization and Applications, Springer, vol. 51(3), pages 1065-1088, April.
    5. Yair Censor & Alexander J. Zaslavski, 2015. "Strict Fejér Monotonicity by Superiorization of Feasibility-Seeking Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 172-187, April.
    Full references (including those not matched with items on IDEAS)

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