Parametric Variational System with a Smooth-Boundary Constraint Set
Solution stability of parametric variational systems with smooth-boundary constraint sets is investigated. Sufficient conditions for the lower semicontinuity, Lipschitz-like property, and local metric regularity in Robinson’s sense of the solution map are obtained by using a calculus rule for the normal second-order subdifferential from B.S. Mordukhovich (Variational Analysis and Generalized Differentiation, Vol.I: Basic Theory, Vol.II: Applications, Springer, Berlin, 2006) and the implicit function theorems for multifunctions from G.M. Lee, N.N. Tam and N.D. Yen (J Math Anal Appl 338:11–22, 2008).
KeywordsBanach Space Variational Inequality Lower Semicontinuous Implicit Function Theorem Norm Topology
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This work was supported by the National Sun Yat-Sen University, Kaohsiung, Taiwan and the National Foundation for Science & Technology Development, Vietnam. The authors are indebted to Dr. N.Q. Huy, Mr. N.H. Chieu and Mr. T.D. Chuong for an useful discussion on Asplund spaces. We thank the referee for helpful comments.
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