Publications (11) View all
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Dataset: KLWY-EJOR-revised
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Article: On the Solution Existence of Generalized Quasivariational Inequalities with Discontinuous Multifunctions
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ABSTRACT: We study the following generalized quasivariational inequality problem: given a closed convex set X in a normed space E with the dual E *, a multifunction F:X® 2E*\Phi :X\rightarrow 2^{E^{*}} and a multifunction Γ:X→2 X , find a point ([^(x)],[^(z)]) Î XE*(\hat{x},\hat{z})\in X\times E^{*} such that [^(x)] Î G([^(x)]),[^(z)] Î F([^(x)]),á[^(z)],[^(x)]-yñ £ 0\hat{x}\in \Gamma(\hat{x}),\hat{z}\in \Phi (\hat{x}),\langle \hat{z},\hat{x}-y\rangle \leq 0 , "y Î G([^(x)])\forall y\in \Gamma(\hat{x}) . We prove some existence theorems in which Φ may be discontinuous, X may be unbounded, and Γ is not assumed to be Hausdorff lower semicontinuous.Journal of Optimization Theory and Applications 04/2012; 135(3):515-530. · 1.06 Impact Factor -
Article: Solution Existence of Variational Inequalities with Pseudomonotone Operators in the Sense of Brézis
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ABSTRACT: This paper is concerned with the study of the solution existence of variational inequalities and generalized variational inequalities in reflexive Banach spaces with pseudomonotone operators in the sense of Brézis. The obtained results cover some preceding results in Browder (J. Funct. Anal. 11:251–294,1972), Brézis (Ann. Inst. Fourier 18:115–175,1968), Kinderlehrer and Stampacchia (An Introduction to Variational Inequalities and Their Applications, Academic Press, San Diego,1980), Zeidler (Nonlinear Functional Analysis and Its Applications, II/B, Springer, Berlin,1990).Journal of Optimization Theory and Applications 04/2012; 140(2):249-263. · 1.06 Impact Factor -
Article: On the solution stability of variational inequalities
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ABSTRACT: In the present paper, we will study the solution stability of parametric variational conditions 0 Î f(m, x)+ NK(l)(x),{{0 \in f(\mu, x)+ N_{K(\lambda)}(x)},} where M and Λ are topological spaces, f : M Rn ® Rn{f : M \times R^n \to R^n} is a function, K : L® 2Rn{K : \Lambda\to 2^{R^n}} is a multifunction and N K(λ)(x) is the value at x of the normal cone operator associated with the set K(λ). By using the degree theory and the natural map we show that under certain conditions, the solution map of the problem is lower semicontinuous with respect to parameters (μ,λ). Our results are different versions of Robinson’s results [15] and proved directly without the homeomorphic result between the solution sets.Journal of Global Optimization 04/2012; 39(1):101-111. · 1.20 Impact Factor -
Article: Degree theory for generalized variational inequalities and applications.
European Journal of Operational Research. 01/2009; 192:730-736.
