Abstract
We introduce a new asymptotic function, which is mainly adapted to quasiconvex functions. We establish several properties and calculus rules for this concept and compare it to previous notions of generalized asymptotic functions. Finally, we apply our new definition to quasiconvex optimization problems: we characterize the boundedness of the function, and the nonemptiness and compactness of the set of minimizers. We also provide a sufficient condition for the closedness of the image of a nonempty closed and convex set via a vector-valued function.
| Original language | English |
|---|---|
| Pages (from-to) | 170-186 |
| Number of pages | 17 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 180 |
| Issue number | 1 |
| DOIs | |
| State | Published - 15 Jan 2019 |
Bibliographical note
Publisher Copyright:© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Asymptotic cones
- Asymptotic functions
- Closedness criteria
- Nonconvex optimization
- Quasiconvexity
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics