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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.

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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.

Enno Lenzmann Interpolations inequalities and applications to non linear PDE 1)

Cho, J. Kim and S. Kang, Eds.

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.

Variational inequality

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