Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive Mappings
In this paper, we design two inertial-type subgradient extragradient algorithms with the linear-search process for resolving the two pseudomonotone variational inequality problems (VIPs) of and the common fixed point problem (CFPP) of finite Bregman relatively nonexpansive operators and Bregman rela...
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MDPI AG
2023-08-01
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| Online Access: | https://www.mdpi.com/2075-1680/12/9/832 |
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| author | Cong-Shan Wang Lu-Chuan Ceng Bing Li Sheng-Long Cao Hui-Ying Hu Yun-Shui Liang |
| author_facet | Cong-Shan Wang Lu-Chuan Ceng Bing Li Sheng-Long Cao Hui-Ying Hu Yun-Shui Liang |
| author_sort | Cong-Shan Wang |
| collection | DOAJ |
| description | In this paper, we design two inertial-type subgradient extragradient algorithms with the linear-search process for resolving the two pseudomonotone variational inequality problems (VIPs) of and the common fixed point problem (CFPP) of finite Bregman relatively nonexpansive operators and Bregman relatively demicontractive operators in Banach spaces of both <i>p</i>-uniform convexity and uniform smoothness, which are more general than Hilbert ones. By the aid of suitable restrictions, it is shown that the sequences fabricated by the suggested schemes converge weakly and strongly to a solution of a pair of VIPs with a CFPP constraint, respectively. Additionally, the illustrative instance is furnished to back up the practicability and implementability of the suggested methods. This paper reveals the competitive advantage of the proposed algorithms over the existing algorithms; that is, the existing hybrid projection method for a single VIP with an FPP constraint is extended to develop the modified inertial-type subgradient extragradient method for a pair of VIPs with an CFPP constraint. |
| first_indexed | 2024-03-10T23:02:31Z |
| format | Article |
| id | doaj.art-70a6d879da174ae4b5b8226310cf2fa0 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T23:02:31Z |
| publishDate | 2023-08-01 |
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| record_format | Article |
| series | Axioms |
| spelling | doaj.art-70a6d879da174ae4b5b8226310cf2fa02023-11-19T09:32:20ZengMDPI AGAxioms2075-16802023-08-0112983210.3390/axioms12090832Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive MappingsCong-Shan Wang0Lu-Chuan Ceng1Bing Li2Sheng-Long Cao3Hui-Ying Hu4Yun-Shui Liang5Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaIn this paper, we design two inertial-type subgradient extragradient algorithms with the linear-search process for resolving the two pseudomonotone variational inequality problems (VIPs) of and the common fixed point problem (CFPP) of finite Bregman relatively nonexpansive operators and Bregman relatively demicontractive operators in Banach spaces of both <i>p</i>-uniform convexity and uniform smoothness, which are more general than Hilbert ones. By the aid of suitable restrictions, it is shown that the sequences fabricated by the suggested schemes converge weakly and strongly to a solution of a pair of VIPs with a CFPP constraint, respectively. Additionally, the illustrative instance is furnished to back up the practicability and implementability of the suggested methods. This paper reveals the competitive advantage of the proposed algorithms over the existing algorithms; that is, the existing hybrid projection method for a single VIP with an FPP constraint is extended to develop the modified inertial-type subgradient extragradient method for a pair of VIPs with an CFPP constraint.https://www.mdpi.com/2075-1680/12/9/832modified inertial-type subgradient extragradient methodvariational inequality problemfinite Bregman relatively nonexpansive mappingsBregman relatively demicontractive mappingBregman distanceBregman projection |
| spellingShingle | Cong-Shan Wang Lu-Chuan Ceng Bing Li Sheng-Long Cao Hui-Ying Hu Yun-Shui Liang Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive Mappings Axioms modified inertial-type subgradient extragradient method variational inequality problem finite Bregman relatively nonexpansive mappings Bregman relatively demicontractive mapping Bregman distance Bregman projection |
| title | Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive Mappings |
| title_full | Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive Mappings |
| title_fullStr | Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive Mappings |
| title_full_unstemmed | Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive Mappings |
| title_short | Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive Mappings |
| title_sort | modified inertial type subgradient extragradient methods for variational inequalities and fixed points of finite bregman relatively nonexpansive and demicontractive mappings |
| topic | modified inertial-type subgradient extragradient method variational inequality problem finite Bregman relatively nonexpansive mappings Bregman relatively demicontractive mapping Bregman distance Bregman projection |
| url | https://www.mdpi.com/2075-1680/12/9/832 |
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