Finite-Dimensional Variational and Quasivariational Inequalities: Algorithmic Developments and Applications in Socio-Eoonomic Planning

Abstract

Over the past several years the f inite-dimensional variational inequality problem has been well studied from the perspectives of computation, sensitivity analysis and application. This paper will briefly review the variational inequality literature and will also discuss the finite dimensional quasivariational inequality problem from the above mentioned perspectives. In particular, three recent results will be discussed in detail. First, an acceleration step for the nonlinear Jacobi and projection algorithms will be presented along with empirical results. Second, a special case of the quasivariational inequality problem which arises in pseudo-Nash or social equilibria games is studied in detail. Characterizations of the solutions of such problems and their relationships with variational inequality solution are presented along with some results on the stability and sensitivity of these solutions. Finally, the theory and empirical validation of a restricted simplicial decomposition algorithm for large-scale, linearly-constrained variational inequalities will be described.