The continued growth and expanded applications in engineering, economics, and sciences have greatly increased the need for advanced computational methods for solving some highly complex nonlinear complementary problems and variational inequalities. The proposed investigation will focus on several major aspects: (a) foundational---convergence properties and posteriori error analysis of new and existing solution methods, (b) numerical--- computer implementation and testing and software development of new algorithms, and (c) practical---the efficient solution of important classes of engineering and economics problems. The class of mathematical programs with equilibrium constraints will also be investigated. ***
