Self adaptive alternated inertial algorithm for solving variational inequality and fixed point problems

Yuanheng Wang; Chenjing Wu; Yekini Shehu; Bin Huang; Yuanheng Wang; Chenjing Wu; Yekini Shehu; Bin Huang

doi:10.3934/math.2024475

AIMS Mathematics

2024, Volume 9, Issue 4: 9705-9720. doi: 10.3934/math.2024475

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Self adaptive alternated inertial algorithm for solving variational inequality and fixed point problems

School of Mathematical Science, Zhejiang Normal University, Jinhua 321004, China

Received: 13 January 2024 Revised: 01 March 2024 Accepted: 07 March 2024 Published: 11 March 2024
MSC : 47H04, 47H09, 47H10, 65K10

We introduce an alternated inertial subgradient extragradient algorithm of non-Lipschitz and pseudo-monotone operators to solve variational inequality and fixed point problems. We also demonstrated that, under certain conditions, the sequence produced by our algorithm exhibits weak convergence. Moreover, some numerical experiments have been proposed to compare our algorithm with previous algorithms in order to demonstrate the effectiveness of our algorithm.
- fixed point,
- self adaptive stepsize,
- alternated inertial,
- variational inequality
Citation: Yuanheng Wang, Chenjing Wu, Yekini Shehu, Bin Huang. Self adaptive alternated inertial algorithm for solving variational inequality and fixed point problems[J]. AIMS Mathematics, 2024, 9(4): 9705-9720. doi: 10.3934/math.2024475

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Abstract

We introduce an alternated inertial subgradient extragradient algorithm of non-Lipschitz and pseudo-monotone operators to solve variational inequality and fixed point problems. We also demonstrated that, under certain conditions, the sequence produced by our algorithm exhibits weak convergence. Moreover, some numerical experiments have been proposed to compare our algorithm with previous algorithms in order to demonstrate the effectiveness of our algorithm.

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