Variational Inequality (VI) Methods for Multiuser Communication Systems and Smart Grids

The Variation Inequality (VI) problem constitutes a very general class of problems in nonlinear analysis. The VI framework embraces many different types of problems such as systems of equations, optimization problems, equilibrium programming, complementary problems, saddle-point problems, Nash equilibrium problems, and generalized Nash equilibrium problems. It specially bears strong connections with game theory. There is a well-developed theory for the analysis of solutions of VIs, as well as a wide variety of efficient algorithms with convergence properties. Therefore, it constitutes an excellent tool for analyzing the previous problems and, in particular, game problems where the classical game-theoretic tools may fall short like in advanced cognitive radio systems.