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AIMS Mathematics

2023, Volume 8, Issue 3: 6389-6406. doi: 10.3934/math.2023323
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Research article

Alternating direction method for the fixed point problem of set-valued mappings with second-order cone double constraints

  • School of Science, Shenyang Aerospace University, Shenyang 110136, China
  • Received: 06 September 2022 Revised: 28 November 2022 Accepted: 08 December 2022 Published: 03 January 2023

  • MSC : 37C25, 65K99

  • This paper focuses on solving a class of equilibrium problems, namely, the fixed point problem of set-valued mappings with second-order cone double constraints. Under certain conditions, the variational inequality form of the fixed point problem of set-valued mappings with second-order cone double constraints is obtained by using the generalized saddle point theory three times. The alternating direction method is used to solve the fixed point problem of set-valued mappings with second-order cone double constraints, and the global convergence of the algorithm is proved. Finally, numerical results of solving five examples with an inexact alternating direction method are given, and the feasibility and effectiveness of the algorithm are demonstrated by comparing with other algorithms.

    Citation: Na Mi, Juhe Sun, Li Wang, Yu Liu. Alternating direction method for the fixed point problem of set-valued mappings with second-order cone double constraints[J]. AIMS Mathematics, 2023, 8(3): 6389-6406. doi: 10.3934/math.2023323

    Related Papers:

  • This paper focuses on solving a class of equilibrium problems, namely, the fixed point problem of set-valued mappings with second-order cone double constraints. Under certain conditions, the variational inequality form of the fixed point problem of set-valued mappings with second-order cone double constraints is obtained by using the generalized saddle point theory three times. The alternating direction method is used to solve the fixed point problem of set-valued mappings with second-order cone double constraints, and the global convergence of the algorithm is proved. Finally, numerical results of solving five examples with an inexact alternating direction method are given, and the feasibility and effectiveness of the algorithm are demonstrated by comparing with other algorithms.


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