Mathematical Programming

, Volume 143, Issue 1–2, pp 147–176 | Cite as

Chain rules for linear openness in metric spaces and applications

Full Length Paper Series A


In this work we present a general theorem concerning chain rules for linear openness of set-valued mappings acting between metric spaces. As particular cases, we obtain classical and also some new results in this field of research, including the celebrated Lyusternik–Graves Theorem. The applications deal with the study of the well-posedness of the solution mappings associated to parametric systems. Sharp estimates for the involved regularity moduli are given.


Composition of set-valued mappings Linear openness   Metric regularity Aubin property Implicit multifunctions  Local composition-stability Parametric systems 

Mathematics Subject Classification (2010)

47J22 49K40 90C31 



The authors are indebted to the referees for their valuable comments and suggestions. This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS—UEFISCDI, project number PN-II-ID-PCE-2011-3-0084.


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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2012

Authors and Affiliations

  1. 1.Faculty of Mathematics“Al. I. Cuza” UniversityIasiRomania
  2. 2.Department of Mathematics“Gh. Asachi” Technical UniversityIasiRomania

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