On the solution existence of pseudomonotone variational inequalities

Abstract. As shown by Thanh-Hao [11], the solution existence results established by Facchinei and Pang [5, Vol. I, 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 [5, Vol. I] 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. Keywords. Variational inequality, generalized variational inequality, pseudomonotone operator, solution existence, degree theory.

• Type: Journal
• Year: 2008
• Where: JGO
• Authors: B. T. Kien, J. C. Yao, N. D. Yen
• Keywords: JGO 2008, Pseudomonotone Variational Inequalities, Solution Existence, Variational Inequalities