Existence of solutions for a generalized vector quasivariational inequality

Chen, G. Y.; Li, S. J.

doi:10.1007/bf02190001

Cited by 55 publications

(23 citation statements)

References 12 publications

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“…Chen and Cheng [5] proposed the vector variational inequality in an infinite-dimensional space and applied it to the vector optimization problem. Since then, many authors have extensively studied various types of vector variational inequalities in abstract space (see, for example, [4,6,8,9,11,14,21,27,28,30,33,37,38] and the references therein). Recently, some authors have investigated the optimality conditions for vector variational inequalities.…”

Section: Introductionmentioning

confidence: 99%

Optimality conditions for the Henig efficient solution of vector equilibrium problems with constraints

2010

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The purpose of this paper is to establish optimality conditions for vector equilibrium problems with constraints. By using the separation of convex sets, we obtain the necessary and sufficient conditions for the Henig efficient solution and the superefficient solution to the vector equilibrium problem with constraints. As applications of our results, we derive some optimality conditions to the vector variational inequality problem and the vector optimization problem with constraints.

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Section: Introductionmentioning

confidence: 99%

Optimality conditions for the Henig efficient solution of vector equilibrium problems with constraints

2010

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“…Since G is proto-differentiable at (λ,p,x,ẑ), by (8)- (10) we obtain that Q is protodifferentiable at (λ,p,x) and the conclusion holds. …”

Section: Gphk Is a Compact Set) Is Proto-dif Ferentiable At (λX) Anmentioning

confidence: 67%

“…Up to now, many important results of VVIs in various versions have been established, see [12,21] and the references therein. In particular, a great deal of researches have been devoted to existences of solutions to VVIs in various versions, for example, see [9,10,58].…”

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confidence: 99%

Stability and Sensitivity Analysis of Solutions to Weak Vector Variational Inequalities

Fang

2011

Set-Valued Anal

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The paper mainly concerns the study of a parametric weak vector variational inequality. Robinson's metric regularity and Lipschitzian stability of the solution mapping for the parametric weak vector variational inequality are firstly established. Then sensitivity analysis of the solution mapping for the parametric weak vector variational inequality is discussed. As applications, Lipschitzian continuity and differentiability of the solution mapping are also investigated for a parametric variational inequality.Keywords Robinson's metric regularity · Sensitivity analysis · Parametric weak vector variational inequality · Parametric variational inequality Mathematics Subject Classifications (2010) 49J53 · 90C29 · 90C31

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“…Many important results on existences and stabilities for various kinds of vector variational inequalities have been established, see e.g. [3,4,5,7,9,10,15,17] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A method of differential and sensitivity properties for weak vector variational inequalities

Guo¹,

Zeng²,

Sun³

et al. 2015

J. Nonlinear Sci. Appl.

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In this paper, by virtue of a contingent derivative and a Φ-contingent cone, we investigate differential properties of a class of set-valued maps in a more general setting utilizing Hadamard directional differentials. Then, by means of a gap function, sensitivity properties are discussed for a weak vector variational inequality. We also show that our results extend some existing results in the literature.

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Existence of solutions for a generalized vector quasivariational inequality

Cited by 55 publications

References 12 publications

Optimality conditions for the Henig efficient solution of vector equilibrium problems with constraints

Optimality conditions for the Henig efficient solution of vector equilibrium problems with constraints

Stability and Sensitivity Analysis of Solutions to Weak Vector Variational Inequalities

A method of differential and sensitivity properties for weak vector variational inequalities

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