Sensitivity Analysis in Differential Programming through the Clarke Derivative

Guerra, Pedro Jiménez; Padial, Miguel Ángel Melguizo

doi:10.1007/s00009-011-0143-7

Cited by 6 publications

(1 citation statement)

References 14 publications

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“…The paper [22] presented TP-derivative and this derivative was put to use to weaken some assumptions in [10]. 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].…”

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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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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A natural extension of the classical envelope theorem in vector differential programming

García-Castaño

Padial

2015

J Glob Optim

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The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity.

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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 Differential Programming through the Clarke Derivative

Cited by 6 publications

References 14 publications

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

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

A natural extension of the classical envelope theorem in vector differential programming

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

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