Journal of Global Optimization

, Volume 41, Issue 1, pp 135–145 | Cite as

On the solution existence of pseudomonotone variational inequalities

  • B. T. Kien
  • J.-C. Yao
  • N. D. Yen


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.


Variational inequality Generalized variational inequality Pseudomonotone operator Solution existence Degree theory 


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Copyright information

© Springer Science+Business Media, LLC. 2007

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational Sun Yat-Sen UniversityKaohsiungTaiwan
  2. 2.Institute of MathematicsVietnamese Academy of Science and TechnologyHanoiVietnam

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