On the solution existence of pseudomonotone variational inequalities

Authors:
B. T. Kien;J. -C. Yao;N. D. Yen
Affiliations:
Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan 804;Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan 804;Institute of Mathematics, Vietnamese Academy of Science and Technology, Hanoi, Vietnam 10307
Venue:
Journal of Global Optimization
Year:
2008

Citing 4
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Abstract

As shown by Thanh Hao [Acta Math. Vietnam 31, 283---289, 2006], the solution existence results established by Facchinei and Pang [Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. I (Springer, Berlin, 2003) Prop. 2.2.3 and Theorem 2.3.4] for variational inequalities (VIs) in general and for pseudomonotone VIs in particular, are very useful for studying the range of applicability of the Tikhonov regularization method. This paper proposes some extensions of these results of Facchinei and Pang to the case of generalized variational inequalities (GVI) and of variational inequalities in infinite-dimensional reflexive Banach spaces. Various examples are given to analyze in detail the obtained results.