A novel adaptive method for operator inclusions

Автор(и)

  • Vladimir V. Semenov Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv
  • Serhii Denysov Dept. of Computational Mathematics, TSNUK
  • Yana Vedel Dept. of Computational Mathematics, TSNUK

DOI:

https://doi.org/10.31713/MCIT.2021.08

Ключові слова:

maximal monotone operator, operator inclusion, splitting algorithm, adaptability, 2-uniformly convex Banach space, uniformly smooth Banach space

Анотація

A novel splitting algorithm for solving operator inclusion with the sum of the maximal monotone operator and the monotone Lipschitz continuous operator in the Banach space is proposed and studied. The proposed algorithm is an adaptive variant of the forward-reflected-backward algorithm, where the rule used to update the step size does not require knowledge of the Lipschitz constant of the operator. For operator inclusions in 2-uniformly convex and uniformly smooth Banach space, the theorem on the weak convergence of the method is proved.

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Опубліковано

2021-11-21

Як цитувати

Semenov, V. V., Denysov, S., & Vedel, Y. (2021). A novel adaptive method for operator inclusions. Моделювання, керування та інформаційні технології, (5), 33–35. https://doi.org/10.31713/MCIT.2021.08