Pointwise well-posedness in set optimization with cone proper sets

Enrico Miglierina, C. Gutiérrez, E. Miglierina, E. Molho, V. Novo

Research output: Contribution to journalArticlepeer-review

55 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1822-1833
Number of pages12
Publication statusPublished - 2012


  • Gerstewitz’s map
  • Quasiconvex set-valued map
  • Scalarization
  • Set optimization
  • Strict minimizer
  • Well-posedness


Dive into the research topics of 'Pointwise well-posedness in set optimization with cone proper sets'. Together they form a unique fingerprint.

Cite this