On the Efficient Solution of Variational Inequalities; Complexity and Computational Efficiency
Author(s)Perakis, Georgia; Zaretsky, M. (Marina)
In this paper we combine ideas from cutting plane and interior point methods in order to solve variational inequality problems efficiently. In particular, we introduce a general framework that incorporates nonlinear as well as linear "smarter" cuts. These cuts utilize second order information on the problem through the use of a gap function. We establish convergence as well as complexity results for this framework. Moreover, in order to devise more practical methods, we consider an affine scaling method as it applies to symmetric, monotone variationalinequality problems and demonstrate its convergence. Finally, in order to further improve the computational efficiency of the methods in this paper, we combine the cutting plane approach with the affine scaling approach.
Massachusetts Institute of Technology, Operations Research Center
Operations Research Center Working Paper;OR 360-02
Variational inequalities, Interior-point methods, Affine Scaling, Cutting Plane Methods AMS Subject Classifications: Primary 90C06; Secondary 90C25