Abstract
In this paper, we study several interesting basic properties of generalized oriented distance function with respect to co-radiant sets or free disposal sets, which are more general than a cone and play an important role to study quasi-minimal solutions of set optimization problems. In particular, we deal with some special properties, namely, translation property, subadditivity and monotonicity, by using co-radiant sets. Moreover, we investigate several kinds of monotonicity properties by means of nonconvex free disposal sets. As an application, we study some optimality conditions for quasi-minimal solutions of set optimization problems by using generalized oriented distance function. At the end, we give an existence theorem for cone saddle-point for set-valued maps. Several examples are given to verify the validity and effectiveness of the derived results.
| Original language | English |
|---|---|
| Pages (from-to) | 247-279 |
| Number of pages | 33 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 193 |
| Issue number | 1-3 |
| DOIs | |
| State | Published - Jun 2022 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Co-radiant set
- Free disposal set
- Oriented distance function
- Quasi-minimal solutions
- Set optimization
- Set relations
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics