Abstract
In this paper, we utilize the improvement set and the recession cone to introduce the concept of E∞-Benson properly efficient solution of the set-valued equilibrium problems and set-valued optimization problems. We establish scalarization optimality conditions, both linear and nonlinear, for E∞-Benson proper efficiency of the set-valued equilibrium problems and also of the set-valued optimization problems. Based on the linear scalarization, we derive Lagrange multiplier optimality conditions for E∞-Benson proper efficiency of the set-valued equilibrium problems and also of the set-valued optimization problems. Several results obtained in this paper are illustrated by examples. The results obtained in this paper improve and generalize some known results in the literature.
| Original language | English |
|---|---|
| Pages (from-to) | 111-134 |
| Number of pages | 24 |
| Journal | Mathematical Methods of Operations Research |
| Volume | 101 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2025 |
Bibliographical note
Publisher Copyright:© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.
Keywords
- Benson properly efficient solutions
- Equilibrium problems
- Optimality conditions
- Recession cone
ASJC Scopus subject areas
- Software
- General Mathematics
- Management Science and Operations Research
Fingerprint
Dive into the research topics of 'Optimality conditions for Benson proper efficiency of set-valued equilibrium problems'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver