A Cutting Hyperplane Projection Method for Solving Generalized Quasi-Variational Inequalities

The generalized quasi-variational inequality is a generalization of the generalized variational inequality and the quasi-variational inequality. The study for the generalized quasi-variational inequality is mainly concerned with the solution existence theory. In this paper, we present a cutting hyperplane projection method for solving generalized quasi-variational inequalities. Our method is new even if it reduces to solve the generalized variational inequalities. The global convergence is proved under certain assumptions. Numerical experiments have shown that our method has less total number of iterative steps than the most recent projection-like methods of Zhang et al. (Comput Optim Appl 45:89–109, 2010) for solving quasi-variational inequality problems and outperforms the method of Li and He (J Comput Appl Math 228:212–218, 2009) for solving generalized variational inequality problems. © 2016, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.