Alternating direction method for the fixed point problem of set-valued mappings with second-order cone double constraints
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 c...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023323?viewType=HTML |
| _version_ | 1811176122971324416 |
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| author | Na Mi Juhe Sun Li Wang Yu Liu |
| author_facet | Na Mi Juhe Sun Li Wang Yu Liu |
| author_sort | Na Mi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T19:48:07Z |
| format | Article |
| id | doaj.art-1679104875524fea8fcab0affe1259ca |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T19:48:07Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-1679104875524fea8fcab0affe1259ca2023-01-29T02:00:55ZengAIMS PressAIMS Mathematics2473-69882023-01-01836389640610.3934/math.2023323Alternating direction method for the fixed point problem of set-valued mappings with second-order cone double constraintsNa Mi0Juhe Sun 1Li Wang2Yu Liu3School of Science, Shenyang Aerospace University, Shenyang 110136, ChinaSchool of Science, Shenyang Aerospace University, Shenyang 110136, ChinaSchool of Science, Shenyang Aerospace University, Shenyang 110136, ChinaSchool of Science, Shenyang Aerospace University, Shenyang 110136, ChinaThis 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.https://www.aimspress.com/article/doi/10.3934/math.2023323?viewType=HTMLsecond-order conedouble constraintsset-valued mappingfixed pointalternating direction methodglobal convergence |
| spellingShingle | 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 AIMS Mathematics second-order cone double constraints set-valued mapping fixed point alternating direction method global convergence |
| title | Alternating direction method for the fixed point problem of set-valued mappings with second-order cone double constraints |
| title_full | Alternating direction method for the fixed point problem of set-valued mappings with second-order cone double constraints |
| title_fullStr | Alternating direction method for the fixed point problem of set-valued mappings with second-order cone double constraints |
| title_full_unstemmed | Alternating direction method for the fixed point problem of set-valued mappings with second-order cone double constraints |
| title_short | Alternating direction method for the fixed point problem of set-valued mappings with second-order cone double constraints |
| title_sort | alternating direction method for the fixed point problem of set valued mappings with second order cone double constraints |
| topic | second-order cone double constraints set-valued mapping fixed point alternating direction method global convergence |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023323?viewType=HTML |
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