SeMA Journal

, Volume 52, Issue 1, pp 73–96 | Cite as

An overview of second order tangent sets and their application to vector optimization

  • G. Giorgi
  • B. Jiménez
  • V. Novo


We take into consideration the main definitions and properties of second order local approximations of sets (or second order tangent sets or second order variational sets). We shall be mainly concerned with the “second order tangent set”, initially proposed by Kawasaki [32, 33] and extensively studied by Cominetti [15] and by Bonnans and Shapiro [8], and with the “asymptotic second order tangent cone”, initially proposed by Penot [39] and independently by Cambini, Martein and Vlach [10]. As an application we establish second order necessary and second order sufficient optimality conditions in terms of second order approximations of sets, for a vector optimization problem.

Key words

Vector optimization first order tangent cones second order tangent sets second order local approximations second order variational sets second order tangent cones 

AMS subject classifications

90C29 90C30 49K27 49J52 


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Copyright information

© Sociedad Española de Matemática Aplicada 2010

Authors and Affiliations

  1. 1.Faculty of EconomicsUniversità degli Studi di PaviaItaly
  2. 2.Departamento de Matemática AplicadaUniversidad Nacional de Educación a DistanciaSpain

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