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)

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.
Original languageEnglish
Pages (from-to)1822-1833
Number of pages12
JournalNONLINEAR ANALYSIS
Volume75
DOIs
Publication statusPublished - 2012

Keywords

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

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