Journal of Global Optimization

, Volume 56, Issue 2, pp 587–603 | Cite as

Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions



In this paper we give some calculus rules for tangent sets in the sense of Bouligand and Ursescu, as well as for corresponding derivatives of set-valued maps. Both first and second-order objects are envisaged and the assumptions we impose in order to get the calculus are in terms of metric subregularity of the assembly of the initial data. This approach is different from those used in alternative recent papers in literature and allows us to avoid compactness conditions. An application to a special type of vector optimization problems, where the objective is given as the sum of two multifunctions, is presented. Furthermore, also as application, a special attention is paid for the case of perturbation set-valued maps which naturally appear in optimization problems.


Bouligand (contingent) tangent sets Ursescu (adjacent) tangent sets Metric regularity Set-valued derivatives Perturbation maps 

Mathematics Subject Classification (2010)

90C30 49J53 54C60 


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© Springer Science+Business Media, LLC. 2011

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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