Abstract
In this paper, a simplicial algorithm is developed to solve the nonlinear complementarity problem onS n×R m+ . Furthermore, a condition for convergence is formulated. The triangulation which underlies the algorithm is a combination of the V-triangulation ofS n and the K-triangulation ofR m+ . Therefore, we will call it the VK-triangulation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Van Der Laan, G., andTalman, A. J. J.,On the Computation of Fixed Points in the Product Space of Unit Simplices and an Application to Noncooperative N-Person Games, Mathematics of Operations Research, Vol. 7, pp. 1–13, 1982.
Doup, T. M.,Simplicial Algorithms on the Simplotope, PhD Dissertation, Tilburg University, Tilburg, Holland, 1987.
Dirven, C. A. J. M., andTalman, A. J. J.,A Simplicial Algorithm for Finding Equilibria in Economies with Linear Production, Research Memorandum No. 271, Department of Economics, Tilburg University, Tilburg, Holland, 1987.
Doup, T. M., andTalman, A. J. J.,A New Simplicial Variable-Dimension Algorithm to Find Equilibria on the Product Space of Unit Simplices, Mathematical Programming, Vol. 37, pp. 319–355, 1987.
Freudenthal, H.,Simplizialzerlegungen von Beschränkter Flachheit, Annals of Mathematics, Vol. 43, pp. 580–582, 1942.
Author information
Authors and Affiliations
Additional information
Communicated by F. Zirilli
The author wishes to thank Professor G. van der Laan for his valuable comments.
Rights and permissions
About this article
Cite this article
Hofkes, M.W. Simplicial algorithm to solve the nonlinear complementarity problem onS n×R m+ . J Optim Theory Appl 67, 551–565 (1990). https://doi.org/10.1007/BF00939649
Issue Date:
DOI: https://doi.org/10.1007/BF00939649