Abstract
We show by an example that, in a complementarity problem where the given map is continuous and monotone on the nonnegative orthant, the existence of a feasible solution is not sufficient to guarantee existence of a solution to the complementarity problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
More, J.,Classes of Functions and Feasibility Conditions in Nonlinear Complementarity Problems, Mathematical Programming, Vol. 6, pp. 327–338, 1974.
Karamardian, S.,Complementarity Problems over Cones with Monotone and Pseudomonotone Maps, Journal of Optimization Theory and Applications, Vol. 18, No. 4, 1976.
Karamardian, S.,The Nonlinear Complementarity Problem with Applications, Part 1, Journal of Optimization Theory and Applications, Vol. 4, No. 2, 1969.
Author information
Authors and Affiliations
Additional information
Communicated by S. Karamardian
The author thanks Professor S. Karamardian and Dr. J. More for helpful discussions regarding this note.
Rights and permissions
About this article
Cite this article
Garcia, C.B. A note on the complementarity problem. J Optim Theory Appl 21, 529–530 (1977). https://doi.org/10.1007/BF00933096
Issue Date:
DOI: https://doi.org/10.1007/BF00933096