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Comments on “The Proximal Point Algorithm Revisited”

Author

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  • Yunda Dong

    (Zhengzhou University)

Abstract

Very recently, the author gave an upper bound on a decreasing positive sequence. And, he made use of it to improve a classical result of Brézis and Lions concerning the proximal point algorithm for monotone inclusion in an infinite-dimensional Hilbert space. One assumption is the algorithm’s strong convergence. In this paper, we derive a new upper bound on this decreasing positive sequence and thus achieve the same improvement without requiring this assumption.

Suggested Citation

  • Yunda Dong, 2015. "Comments on “The Proximal Point Algorithm Revisited”," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 343-349, July.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:1:d:10.1007_s10957-014-0685-5
    DOI: 10.1007/s10957-014-0685-5
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    References listed on IDEAS

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    1. A. J. Zaslavski, 2011. "Maximal Monotone Operators and the Proximal Point Algorithm in the Presence of Computational Errors," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 20-32, July.
    2. Yunda Dong, 2014. "The Proximal Point Algorithm Revisited," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 478-489, May.
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    Cited by:

    1. Eike Börgens & Christian Kanzow, 2019. "Regularized Jacobi-type ADMM-methods for a class of separable convex optimization problems in Hilbert spaces," Computational Optimization and Applications, Springer, vol. 73(3), pages 755-790, July.
    2. J. Preininger & P. T. Vuong, 2018. "On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions," Computational Optimization and Applications, Springer, vol. 70(1), pages 221-238, May.

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    1. Eike Börgens & Christian Kanzow, 2019. "Regularized Jacobi-type ADMM-methods for a class of separable convex optimization problems in Hilbert spaces," Computational Optimization and Applications, Springer, vol. 73(3), pages 755-790, July.
    2. Yunda Dong, 2021. "Weak convergence of an extended splitting method for monotone inclusions," Journal of Global Optimization, Springer, vol. 79(1), pages 257-277, January.
    3. Yunda Dong, 2014. "The Proximal Point Algorithm Revisited," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 478-489, May.

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