On the lower semicontinuity of optimal solution sets

Kien, B. T.

doi:10.1080/02331930412331330379

Cited by 48 publications

(21 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, some examples are provided for illustrating the presented results. The results presented in this article develop, extend and improve the some main results given in [29][30][31][32][33][34][35]37].…”

Section: Introductionmentioning

confidence: 97%

“…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%

“…Zhao [32] obtained a sufficient and necessary condition (H1) for the Hausdorff lower semi-continuity of the solution mapping to a parametric optimization problems. 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%

“…Motivated and inspired by the studies reported in [29][30][31][32][33][34][35][36][37], the aim of this article is to investigate a class of (PGVQVLIP) in Hausdorff topological vector spaces, where the constraint set K and a set-valued mapping T are perturbed by different parameters. We establish the nonemptiness and upper semi-continuity of the solution mapping for (PGVQVLIP) under some suitable conditions.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

et al. 2012

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 97%

“…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%

See 2 more Smart Citations

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

et al. 2012

View full text Add to dashboard Cite

show abstract

“…Later, many authors have investigated vector variational inequality problems in abstract spaces, see [1,13,19,20,24,26,27,29,30,31,35,36,38]. With the development of the theory about vector variational inequality problems, it has been seen that vector variational inequality problems have many important applications in vector optimization problems, see [25,37], vector equilibria problems, see [2,3,4,5,6,7,8,10,11,15,17,21,22,28,32,33,34,39], variational relation problems, see [17,18,23] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On the Lower Semicontinuity of the Solution Sets for Parametric Generalized Vector Mixed Quasivariational Inequality Problems

Hùng¹

2015

Bulletin of the Korean Mathematical Society

View full text Add to dashboard Cite

Abstract. In this paper, we establish sufficient conditions for the solution set of parametric generalized vector mixed quasivariational inequality problem to have the semicontinuities such as the inner-openness, lower semicontinuity and Hausdorff lower semicontinuity. Moreover, a key assumption is introduced by virtue of a parametric gap function by using a nonlinear scalarization function. Then, by using the key assumption, we establish condition (H h (γ 0 , λ 0 , µ 0 )) is a sufficient and necessary condition for the Hausdorff lower semicontinuity, continuity and Hausdorff continuity of the solution set for this problem in Hausdorff topological vector spaces with the objective space being infinite dimensional. The results presented in this paper are different and extend from some main results in the literature.

show abstract

Convergence Analysis of Solution Sets for Minty Vector Quasivariational Inequality Problems in Banach Spaces

Hùng

Hoang

Tâm

et al. 2021

Advances in Metric Fixed Point Theory and Applications

View full text Add to dashboard Cite

On the lower semicontinuity of optimal solution sets

Cited by 48 publications

References 8 publications

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

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

On the Lower Semicontinuity of the Solution Sets for Parametric Generalized Vector Mixed Quasivariational Inequality Problems

Convergence Analysis of Solution Sets for Minty Vector Quasivariational Inequality Problems in Banach Spaces

Contact Info

Product

Resources

About