A note on “Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality” [Positivity. 18, 449–473(2014)]

Xu, Yi; Li, Min; Peng, Zhenhua

doi:10.1007/s11117-015-0355-3

Positivity

2015

DOI: 10.1007/s11117-015-0355-3

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A note on “Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality” [Positivity. 18, 449–473(2014)]

Yi Xu

Min Li

Zhenhua Peng

Abstract: The note points out that the sufficiency of proposition 2.1 in Anh (Positivity 18:449-473, 2014) is erroneous and we provide an example to illustrate it. Also the proof of proposition 2.2 in Anh (Positivity 18:449-473, 2014) is incorrect and we give a new proof.

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Second-order lower radial tangent derivatives and applications to set-valued optimization

Peng

2017

J Inequal Appl

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We introduce the concepts of second-order radial composed tangent derivative, second-order radial tangent derivative, second-order lower radial composed tangent derivative, and second-order lower radial tangent derivative for set-valued maps by means of a radial tangent cone, second-order radial tangent set, lower radial tangent cone, and second-order lower radial tangent set, respectively. Some properties of second-order tangent derivatives are discussed, using which second-order necessary optimality conditions are established for a point pair to be a Henig efficient element of a set-valued optimization problem, and in the expressions the second-order tangent derivatives of the objective function and the constraint function are separated.

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Second-order lower radial tangent derivatives and applications to set-valued optimization

Peng

2017

J Inequal Appl

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A note on “Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality” [Positivity. 18, 449–473(2014)]

Abstract: The note points out that the sufficiency of proposition 2.1 in Anh (Positivity 18:449-473, 2014) is erroneous and we provide an example to illustrate it. Also the proof of proposition 2.2 in Anh (Positivity 18:449-473, 2014) is incorrect and we give a new proof.

Cited by 1 publication

References 5 publications

Second-order lower radial tangent derivatives and applications to set-valued optimization

Second-order lower radial tangent derivatives and applications to set-valued optimization

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