Sensitivity analysis in constrained set-valued optimization via Studniarski derivatives

Anh, Nguyen Le Hoang

doi:10.1007/s11117-016-0418-0

Cited by 16 publications

(2 citation statements)

References 25 publications

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“…In [13], properties of higher-order contingent-type derivatives of the perturbation and weak perturbation maps of a parameterized optimization problem have been obtained by using the higherorder contingent-type derivatives. In [1], Anh has obtained sensitivity results of set-valued optimization problem in terms of Studniarski derivatives. In [2], the higher-order contingent derivative of a parametrized set-valued optimization problem has been studied.…”

Section: Introductionmentioning

confidence: 99%

On second-order radial-asymptotic proto-differentiability of the borwein perturbation maps

Pham¹,

Nguyen²

2022

RAIRO-Oper. Res.

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This paper deals with second-order sensitivity analysis of parameterized vector optimization problems. We prove that the Borwein efficient solution map and the Borwein efficient perturbation map of a parametric vector optimization problem are second-order radial-asymptotic proto-differentiable under some suitable qualification conditions. Some examples are also given for illustrating the obtained results.

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Section: Introductionmentioning

confidence: 99%

On second-order radial-asymptotic proto-differentiability of the borwein perturbation maps

Pham¹,

Nguyen²

2022

RAIRO-Oper. Res.

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“…In [6,9], the Clarke derivatives were employed for analyzing sensitivity. Properties of the contingent derivatives of some types of proper perturbation maps of a parameterized optimization problem were discussed in [1,7,16,23,25]. Some results in the proto-differentiability and semidifferentiability of the perturbation maps were obtained in [11,13,17,26].…”

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis in parametric vector optimization in Banach spaces viaτw-contingent derivatives

Le¹,

Pham²

2020

Turk J Math

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This paper is concerned with sensitivity analysis in parametric vector optimization problems via τ wcontingent derivatives. Firstly, relationships between the τ w-contingent derivative of the Borwein proper perturbation map and the τ w-contingent derivative of feasible map in objective space are considered. Then, the formulas for estimating the τ w-contingent derivative of the Borwein proper perturbation map via the τ w-contingent of the constraint map and the Hadamard derivative of the objective map are obtained.

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Variational sets and asymptotic variational sets of proper perturbation map in parametric vector optimization

Tùng

2017

Positivity

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Sensitivity analysis in constrained set-valued optimization via Studniarski derivatives

Cited by 16 publications

References 25 publications

On second-order radial-asymptotic proto-differentiability of the borwein perturbation maps

On second-order radial-asymptotic proto-differentiability of the borwein perturbation maps

Sensitivity analysis in parametric vector optimization in Banach spaces viaτw-contingent derivatives

Variational sets and asymptotic variational sets of proper perturbation map in parametric vector optimization

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