On the Stability of Generalized Vector Quasivariational Inequality Problems

By S. J. Li, G. Chen, Kok Lay Teo. 2002

98 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1e4790401dc3e69a78521cd968631f48176f6cb3

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Semicontinuity of the Approximate Solution Sets of Multivalued Quasiequilibrium Problems (2008, background): “Lower semicontinuity is studied in [19] for minimization problems, in [12, 16, 17] for variational inequalities, and in [3, 5, 7, 8, 14] for equilibrium problems.”
Lower Semicontinuity and Upper Semicontinuity of the Solution Sets and Approximate Solution Sets of Parametric Multivalued Quasivariational Inequalities (2007, background): “We observed only [13, 15, 16, 20–23] on the lower semicontinuity of the solution set: [20–22] for minimization problems, [23] for generalized inequality systems and [13, 15 , 16] for variational inequalities.”
Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems (2004, methodology): “This corollary improves Theorem 4.1 of [ 23 ], since here K(.)needs not be lsc and (iii3) and (v) need to be fulfilled only at x ∈ S1(λ0) and y ∈ K(λ0).”
Semicontinuity of Solution Sets to Parametric Quasivariational Inclusions with Applications to Traffic Networks II: Lower Semicontinuities Applications (2008, background): “Section 1(d) of Part I] a more special case of (QEPrα), Corollary 3.7 includes Theorems 3.1, 3.2 of Li et al. [ 20 ], Theorem 2.1 of Cheng and Zhu [9], Theorems 2.2, 2.3 of Khanh and Luu [18] and Theorems 4.1, 4.3 of Khanh and Luu [19].”
Sensitivity for parametric vector equilibria (2006, background): “When the solution set is not a singleton, the results of the upper and the lower semicontinuity of the perturbed variational inequality are presented in [7].”
Lower Semicontinuity of the Set of Efficient Solutions for Generalized Systems (2008, background): “For any given μ ∈ and for any given x ∈ A(μ), we have that, for any y, z ∈A(μ), t ∈ [0,1], φ(x, ty + (1 − t)z,μ) = (〈μF1(x), ty + (1 − t)z− x〉, 〈μF2(x), ty + (1 − t)z− x〉) = (〈μF1(x), t (y − x)+ (1 − t)(z− x)〉, 〈μF2(x), t (y − x)+ (1 − t)(z− x)〉) = t (〈μF1(x), y − x〉, 〈μF2(x), y − x〉) + (1 − t)(〈μF1”