Abstract
This short note shows that the existence of solutions of a finite-dimensional monotone variational inequality on a compact set can be proved with only very elementary tools.
This is a preview of subscription content, log in via an institution to check access.
References
Hartman, P., Stampacchia, G.: On some linear elliptic differential equations. Acta Math. 115, 271–310 (1966)
Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problem. Springer, Berlin (2003)
Auslender, A., Teboulle, M.: Asymptotic Cones and Functions in Optimization and Variational Inequalities. Springer, Berlin (2003)
Crouzeix, J.-P., Ocaña, E.: Maximality is nothing but continuity. J. Convex Anal. 17, 521–534 (2010)
Crouzeix, J.-P.: Pseudomonotone variational inequality problems: existence of solutions. Math. Program. 78, 305–314 (1997)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Antonino Maugeri.
Rights and permissions
About this article
Cite this article
Crouzeix, JP. An Elementary Proof of the Existence of Solutions of a Monotone Variational Inequality in the Finite-Dimensional Case. J Optim Theory Appl 168, 441–445 (2016). https://doi.org/10.1007/s10957-015-0760-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10957-015-0760-6