Composite inertial subgradient extragradient methods for variational inequalities and fixed point problems
Abstract In this paper, we introduce and investigate composite inertial gradient-based algorithms with a line-search process for solving a variational inequality problem (VIP) with a pseudomonotone and Lipschitz continuous mapping and a common fixed-point problem (CFPP) of finitely many nonexpansive...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-10-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-019-2229-x |
| _version_ | 1811292956627304448 |
|---|---|
| author | Lu-Chuan Ceng Qing Yuan |
| author_facet | Lu-Chuan Ceng Qing Yuan |
| author_sort | Lu-Chuan Ceng |
| collection | DOAJ |
| description | Abstract In this paper, we introduce and investigate composite inertial gradient-based algorithms with a line-search process for solving a variational inequality problem (VIP) with a pseudomonotone and Lipschitz continuous mapping and a common fixed-point problem (CFPP) of finitely many nonexpansive mappings and a strictly pseudocontractive mapping in the framework infinite-dimensional Hilbert spaces. The proposed algorithms are based on an inertial subgradient–extragradient method with the line-search process, hybrid steepest-descent methods, viscosity approximation methods and Mann iteration methods. Under weak conditions, we prove strong convergence of the proposed algorithms to the element in the common solution set of the VIP and CFPP, which solves a certain hierarchical VIP defined on this common solution set. |
| first_indexed | 2024-04-13T04:54:07Z |
| format | Article |
| id | doaj.art-32d701f2145e47a098a5f7e90d752c39 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-13T04:54:07Z |
| publishDate | 2019-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-32d701f2145e47a098a5f7e90d752c392022-12-22T03:01:34ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-10-012019112010.1186/s13660-019-2229-xComposite inertial subgradient extragradient methods for variational inequalities and fixed point problemsLu-Chuan Ceng0Qing Yuan1Department of Mathematics, Shanghai Normal UniversitySchool of Mathematics and Statistics, Linyi UniversityAbstract In this paper, we introduce and investigate composite inertial gradient-based algorithms with a line-search process for solving a variational inequality problem (VIP) with a pseudomonotone and Lipschitz continuous mapping and a common fixed-point problem (CFPP) of finitely many nonexpansive mappings and a strictly pseudocontractive mapping in the framework infinite-dimensional Hilbert spaces. The proposed algorithms are based on an inertial subgradient–extragradient method with the line-search process, hybrid steepest-descent methods, viscosity approximation methods and Mann iteration methods. Under weak conditions, we prove strong convergence of the proposed algorithms to the element in the common solution set of the VIP and CFPP, which solves a certain hierarchical VIP defined on this common solution set.http://link.springer.com/article/10.1186/s13660-019-2229-xSubgradient–extragradient methodPseudomonotone variational inequality problemCommon fixed-point problemStrictly pseudocontractive mapping |
| spellingShingle | Lu-Chuan Ceng Qing Yuan Composite inertial subgradient extragradient methods for variational inequalities and fixed point problems Journal of Inequalities and Applications Subgradient–extragradient method Pseudomonotone variational inequality problem Common fixed-point problem Strictly pseudocontractive mapping |
| title | Composite inertial subgradient extragradient methods for variational inequalities and fixed point problems |
| title_full | Composite inertial subgradient extragradient methods for variational inequalities and fixed point problems |
| title_fullStr | Composite inertial subgradient extragradient methods for variational inequalities and fixed point problems |
| title_full_unstemmed | Composite inertial subgradient extragradient methods for variational inequalities and fixed point problems |
| title_short | Composite inertial subgradient extragradient methods for variational inequalities and fixed point problems |
| title_sort | composite inertial subgradient extragradient methods for variational inequalities and fixed point problems |
| topic | Subgradient–extragradient method Pseudomonotone variational inequality problem Common fixed-point problem Strictly pseudocontractive mapping |
| url | http://link.springer.com/article/10.1186/s13660-019-2229-x |
| work_keys_str_mv | AT luchuanceng compositeinertialsubgradientextragradientmethodsforvariationalinequalitiesandfixedpointproblems AT qingyuan compositeinertialsubgradientextragradientmethodsforvariationalinequalitiesandfixedpointproblems |