Definition 1. In general, the variational inequality problem can be formulated on any finite — or infinite - dimensional Banach space. The three obvious steps in the study of the problem are the following ones:. This is a standard example problem, reported by Antman , p.
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Three cases can occur:. The absolute minimum must be searched between the solutions if more than one of the preceding inequality : note that the solution is a real number , therefore this is a finite dimensional variational inequality. Optim Theory Appl.
Yao, Bui Trong Kien , Covering properties at positive-order rates of multifunctions and some related topics, J. Yao, Vertical tangent vectors to the graph of a multifunction, Taiwanese Journal of Mathematics, 12 , Nonlinear Convex Anal. Global Optim. Nam, Nguyen Dong Yen , Frechet subdifferential calculus and optimality conditions in nondifferentiable programming, Optimization 55 , - Tam, Nguyen Dong Yen , Continuity of the solution map in quadratic programs under linear perturbations, J.
Theory Appl. Nonlinear Anal. Forum 9 , - Jeyakumar, Nguyen Dong Yen , Solution stability of nonsmooth continuous systems with applications to cone-constrained optimization.
SIAM J. Tam, Nguyen Dong Yen , Some recent results on quadratic programs and affine variational inequality problems under linear perturbations, In: Fixed point theory and applications, Vol.
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Publications on Analysis and Numerical Solution of Variational Inequalities
Ricceri on variational inequalities, In: Fixed point theory and applications, Vol. In: Equilibrium problems and variational models Erice, , - , Nonconvex Optim. In: Fixed point theory and applications, Vol. Lee, Nguyen Dong Yen , A result on vector variational inequalities with polyhedral constraint sets. A, - Cho, Ed. Mathematical Theories F. Giannessi, Ed.
Vietnam J. Mathematical Theories", F. Powered by.
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