Abstract
We present an iterative algorithm for solving variational inequalities under the weakest monotonicity condition proposed so far. The method relies on a new cutting plane and on analytic centers.
Similar content being viewed by others
References
A. Auslender, “Optimisation. Méthodes numériques,” Masson: Paris, 1976.
J.-L. Goffin, Z.Q. Luo, and Y. Ye, “Complexity analysis of an interior cutting plane method for convex feasibility problems,” SIAM Journal on Optimization, vol.6, pp. 638–652, 1996.
J.-L. Goffin, P. Marcotte, and D.L. Zhu, “An analytic center cutting plane method for pseudomonotone variational inequalities,” Operations Research Letters, vol. 20, pp.1–6,1997.
H. Hadjisavvas and S. Schaible, “Quasimonotone variational inequalities in Banach spaces,” Journal of Optimization Theory and Applications, vol. 90, pp.95–111, 1996.
P.T. Harker and J.-S. Pang, “Finite-dimensional variational inequality and non-linear complementarity problems: A survey of theory, algorithms and applications,” Mathematical Programming B, vol.48, pp.161–220, 1990.
D. Kinderlehrer and G. Stampacchia An Introduction to Variational Inequalities and their Applications, Academic Press: New York,1980.
T.L. Magnanti and G. Perakis, “A unifying geometric framework for solving variational inequalities,” Mathematical Programming, vol. 71, pp. 327–351, 1995.
D.L. Zhu and P. Marcotte, “An extended descent framework for monotone variational inequalities,” Journal of Optimization Theory and Applications, vol. 80, pp.349–366, 1994.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Marcotte, P., Zhu, D. A Cutting Plane Method for Solving Quasimonotone Variational Inequalities. Computational Optimization and Applications 20, 317–324 (2001). https://doi.org/10.1023/A:1011219303531
Issue Date:
DOI: https://doi.org/10.1023/A:1011219303531