Abstract
This paper introduces a new class of equilibrium problems called regularized nonconvex mixed equilibrium problems involving two nonlinear bifunctions. By using the auxiliary principle technique, some iterative algorithms for solving them are proposed and analyzed. The study of convergence analysis of the proposed iterative algorithms requires only either joint pseudomonotonicity or partially mixed relaxed and strong monotonicity of the bifunctions involved in the considered problem. As a consequence of our main results, we provide the correct versions of the algorithms and results presented in the literature.
| Original language | English |
|---|---|
| Pages (from-to) | 607-622 |
| Number of pages | 16 |
| Journal | Journal of Nonlinear and Convex Analysis |
| Volume | 18 |
| Issue number | 4 |
| State | Published - 2017 |
Bibliographical note
Publisher Copyright:© 2017.
Keywords
- Auxiliary principle technique
- Convergence analysis
- Nonconvex equilibrium problems
- Nonconvex sets
- Predictor-corrector methods
- Prox-regularity
- Regularized mixed equilibrium problems
ASJC Scopus subject areas
- Analysis
- Geometry and Topology
- Control and Optimization
- Applied Mathematics