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Effect of shrinking projection and CQ-methods on two inertial forward–backward algorithms for solving variational inclusion problems

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Abstract

In this paper, we establish the convergence theorems for two projection algorithms for finding a null point of the sum of two monotone operators in Hilbert spaces. Our algorithms are the combination the inertial forward–backward with the shrinking of hybrid projection methods. To clarify the acceleration, effectiveness, and performance of proposed algorithms, numerical contributions have been incorporated.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Thai Nguyen University of Sciences, Thái Nguyên, Vietnam

    Truong Minh Tuyen

  2. Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, Egypt

    Hasanen A. Hammad

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  1. Truong Minh Tuyen
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  2. Hasanen A. Hammad
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Correspondence to Hasanen A. Hammad.

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Tuyen, T.M., Hammad, H.A. Effect of shrinking projection and CQ-methods on two inertial forward–backward algorithms for solving variational inclusion problems. Rend. Circ. Mat. Palermo, II. Ser 70, 1669–1683 (2021). https://doi.org/10.1007/s12215-020-00581-8

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