Abstract
The main goal of this paper is to introduce and study bilevel vector equilibrium problems. We first establish some existence results for solutions of vector equilibrium problems and mixed vector equilibrium problems. We study the existence of solutions of bilevel vector equilibrium problems by considering a vector Thikhonov-type regularization procedure. By using this regularization procedure and existence results for mixed vector equilibrium problems, we establish some existence results for solutions of bilevel vector equilibrium problems. By using the auxiliary principle, we propose an algorithm for finding the approximate solutions of bilevel vector equilibrium problems. The strong convergence of the proposed algorithm is also studied.
| Original language | English |
|---|---|
| Pages (from-to) | 726-758 |
| Number of pages | 33 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 172 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 Mar 2017 |
Bibliographical note
Publisher Copyright:© 2017, Springer Science+Business Media New York.
Keywords
- Auxiliary principle
- Bilevel programs
- Bilevel vector equilibrium problems
- C-convex functions
- C-maximal bifunctions
- C-monotone bifunctions
- C-upper (lower) semicontinuity
- Convergence analysis
- Mixed vector equilibrium problems
- Vector equilibrium problems
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics