Set-Valued and Variational Analysis

, Volume 26, Issue 3, pp 561–579 | Cite as

On Second-Order Proto-Differentiability of Perturbation Maps

  • L. T. TungEmail author


In this paper, second-order sensitivity analysis in vector optimization problems is considered. We prove that the efficient solution map and the efficient frontier map of a parameterized vector optimization problem are second-order proto-differentiable under some appropriate qualification conditions. Some sufficient conditions for inner and outer approximation of the second-order proto-derivative are also provided.


Second-order proto-differentiability Second-order semi-differentiability Parameterized vector optimization problems Solution maps Frontier maps Second-order sensitivity analysis 

Mathematics Subject Classifications (2010)

90C46 49J52 46G05 90C26 90C29 


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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Mathematics, College of Natural SciencesCantho UniversityCanthoVietnam

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