Abstract
This paper deals with the well-posedness property in the setting of set optimization problems. By using a notion of well-posed set optimization problem due to Zhang et al. (2009) and a scalarization process, we characterize this property through the well-posedness, in the Tykhonov sense, of a family of scalar optimization problems and we show that certain quasiconvex set optimization problems are well-posed. Our approach is based just on a weak boundedness assumption, called cone properness, that is unavoidable to obtain a meaningful set optimization problem.
Lingua originale | English |
---|---|
pagine (da-a) | 1822-1833 |
Numero di pagine | 12 |
Rivista | NONLINEAR ANALYSIS |
Volume | 75 |
DOI | |
Stato di pubblicazione | Pubblicato - 2012 |
Keywords
- Gerstewitz’s map
- Quasiconvex set-valued map
- Scalarization
- Set optimization
- Strict minimizer
- Well-posedness