Stability Results of Variational Systems Under Openness with Respect to Fixed Sets

Monica Bianchi, G. Kassay, R. Pini

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper we present the notions of (U; V )-openness and (U; V )- metric regularity for a set-valued map, proving their equivalence. By using different approaches we show the stability, with respect to the sum of maps, of the (U; V )-openness property, both in the setting of Banach spaces, and of metric spaces. Finally, we infer the regularity of the map solving a generalized parametric equation defined via a parametric map that is, in its turn, perturbed by the sum with another map.
Original languageEnglish
Pages (from-to)92-108
Number of pages17
JournalJournal of Optimization Theory and Applications
DOIs
Publication statusPublished - 2015

Keywords

  • Generalized equation
  • Linear openness
  • Sum of maps

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