Solving Quasi-Variational Inequalities Using the Progressive Decoupling of Linkages

Abstract

Inspired by the progressive decoupling of linkages methodology for optimization and variational inequalities, we propose an algorithm for solving quasi-variational inequalities as a sequence of variational inequalities. Our method is shown to converge locally under some regularity conditions and globally when such conditions hold throughout the entire domain. Separately, under other type of assumptions, global convergence with linear rate is also established for the class of quasi-variational inequalities said to have a moving set. Advantageous computational performance is shown for large-scale Walrasian equilibrium problems, a special case of generalized Nash equilibria, as well as for some other instances encountered in related literature.