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On the solution existence of pseudomonotone variational inequalities

An Erratum to this article was published on 24 October 2007

Abstract

As shown by N. Thanh Hao (submitted data), the solution existence results established by F. Facchinei and J.-S. Pang [(vols. I, II, Springer, Berlin, 2003) Prop. 2.2.3 and Theorem 2.3.4] for variational inequalities in general and for pseudomonotone variational inequalities 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 (Finite-Dimensional Variational Inequalities and Complementarity Problems, vols. I, II, Springer, 2003) to the case of generalized variational inequalities and of variational inequalities in infinite-dimensional reflexive Banach spaces. Various examples are given to analyze in detail the obtained results.

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Correspondence to J. -C. Yao.

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B.T. Kien – on leave from the Hanoi University of Civil Engineering.

An erratum to this article is available at http://dx.doi.org/10.1007/s10898-007-9251-0.

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Kien, B.T., Yao, J.C. & Yen, N.D. On the solution existence of pseudomonotone variational inequalities. J Glob Optim (2007). https://doi.org/10.1007/s10898-007-9170-0

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  • DOI: https://doi.org/10.1007/s10898-007-9170-0

Keywords

  • Variational inequality
  • Generalized variational inequality
  • Pseudomonotone operator
  • Solution existence
  • Degree theory