Abstract
In this paper, we consider set optimization problems whose solution concepts are defined by means of set less order relations involving Minkwoski difference. We propose well-posedness and generalized well-posedness for set optimization problems, and derive sufficient and necessary conditions for these well-posedness. A relation between well-posedness and generalized well-posedness for set optimization problems is also given. We use a nonlinear scalarization method to establish necessary and sufficient conditions for the well-posedness and generalized well-posedness of set optimization problems. Several examples are given to illustrate our results.
| Original language | English |
|---|---|
| Article number | 31 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 204 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 2025 |
Bibliographical note
Publisher Copyright:© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
Keywords
- Scalarization
- Set optimization problems
- Set order relations
- Well-posedness
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics
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