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- Title
Convergence Analysis of Self-Adaptive Inertial Extra-Gradient Method for Solving a Family of Pseudomonotone Equilibrium Problems with Application.
- Authors
Bantaojai, Thanatporn; Pakkaranang, Nuttapol; ur Rehman, Habib; Kumam, Poom; Kumam, Wiyada
- Abstract
In this article, we propose a new modified extragradient-like method to solve pseudomonotone equilibrium problems in real Hilbert space with a Lipschitz-type condition on a bifunction. This method uses a variable stepsize formula that is updated at each iteration based on the previous iterations. The advantage of the method is that it operates without prior knowledge of Lipschitz-type constants and any line search method. The weak convergence of the method is established by taking mild conditions on a bifunction. In the context of an application, fixed-point theorems involving strict pseudo-contraction and results for pseudomonotone variational inequalities are considered. Many numerical results have been reported to explain the numerical behavior of the proposed method.
- Subjects
HILBERT space; EQUILIBRIUM; VARIATIONAL inequalities (Mathematics); PRIOR learning; FAMILIES
- Publication
Symmetry (20738994), 2020, Vol 12, Issue 8, p1332
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym12081332