Stability of weak vector variational inequality

Li, S.J.; Chen, C.R.

doi:10.1016/j.na.2008.02.032

Cited by 48 publications

(39 citation statements)

References 12 publications

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“…Remark 3.5. As pointed in [21,32,34,35], the hypothesis (Hg)" can be explained by the geometric properties that, for any small positive number , one can take two small positive real number ϱ and δ such that, for all problems in the δ-neighborhood of a pair parameters (l 0 , μ 0 ), if a feasible point x is away from the solution set by a distance of at least , then a "gap" by an amount of at least -ϱ will be generated. As mentioned out in [32], the above hypothesis (Hg)" is characterized by a common theme used in mathematical analysis.…”

Section: T(x μ) η(Yx) + φ(Yx) / ∈ −Int C(x) ∀Y ∈ K(λ) (3:5)mentioning

confidence: 82%

“…Motivated by the hypothesis (H 1 ) of [32,33], (Hg) of [21,34] and (Hg)' of [35], by virtue of the parametric gap function g, we also introduce the following key assumption:…”

Section: T(x μ) η(Yx) + φ(Yx) / ∈ −Int C(x) ∀Y ∈ K(λ) (3:5)mentioning

confidence: 99%

“…Especially, some authors have tried to discuss the upper and lower semi-continuity of solution mappings (see, for instance, [19][20][21][22][23][24][25][26][27][28] and the reference therein). Khanh and Luu [29] studied a parametric multi-valued quasi-variational inequalities and obtained the semi-continuity of the solution sets and approximate solution sets.…”

Section: Introductionmentioning

confidence: 99%

“…Under mild assumptions, Kien [33] also obtained the sufficient and necessary condition (H1) for the Hausdorff lower semicontinuity of the solution mapping to a parametric optimization problems. By using a condition (Hg) similar to it given in [32], Li and Chen [21] proved that (Hg) is also sufficient for the Hausdorff lower semi-continuity of the solution mapping to a class of weak vector variational inequality.…”

Section: Introductionmentioning

confidence: 99%

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Stability analysis for parametric generalized vector quasi-variational-like inequality problems

et al. 2012

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In this article, we consider a class of parametric generalized vector quasi-variationallike inequality problem (for short, (PGVQVLIP)) in Hausdorff topological vector spaces, where the constraint set K and a set-valued mapping T are perturbed by different parameters, and establish the nonemptiness and upper semicontinuity of the solution mapping S for (PGVQVLIP) under some suitable conditions. By virtue of the gap function, sufficient conditions for the H-continuity and B-continuity of the solution mapping S of (PGVQVLIP) are also derived. Moreover, examples are provided for illustrating the presented results. 2000 Mathematics Subject Classification: 49J40; 90C33.

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Section: T(x μ) η(Yx) + φ(Yx) / ∈ −Int C(x) ∀Y ∈ K(λ) (3:5)mentioning

confidence: 82%

“…Motivated by the hypothesis (H 1 ) of [32,33], (Hg) of [21,34] and (Hg)' of [35], by virtue of the parametric gap function g, we also introduce the following key assumption:…”

Section: T(x μ) η(Yx) + φ(Yx) / ∈ −Int C(x) ∀Y ∈ K(λ) (3:5)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stability analysis for parametric generalized vector quasi-variational-like inequality problems

et al. 2012

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“…The stability analysis of solution maps for equilibrium problems is an important topic in optimization theory and applications. There have been many papers to discuss the semicontinuity of solution maps (see [1,4,6,7,13,15,16]). However, there are only a few results concerning the Hölder continuity of solution maps for the perturbed variational inequality and equilibrium problems.…”

Section: Introductionmentioning

confidence: 99%