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.
Miglierina, E., Gutiérrez, C., Molho, E., Novo, V., Pointwise well-posedness in set optimization with cone proper sets, <<NONLINEAR ANALYSIS>>, 2012; 75 (4): 1822-1833. [doi:10.1016/j.na.2011.09.028] [http://dx.medra.org/10.1016/j.na.2011.09.028] [http://hdl.handle.net/10807/1424]
Pointwise well-posedness in set optimization with cone proper sets
Miglierina, Enrico;
2012
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.
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