A general descent framework for the monotone variational inequality problem

The authors present a framework for descent algorithms that solve the monotone variational inequality problem VIPÅv which consists in finding a solution v*∈¦[v satisfying s(v*)’T(v-v*)∈0, for all v∈¦[v. This unified framework includes, as special cases, some well known iterative methods and equivalent optimization formulations. A descent method is developed for an equivalent general optimization formulation and a proof of its convergence is given. Based on this unified logarithmic framework, the authors show that a variant of the descent method where each subproblem is only solved approximately is globally convergent under certain conditions.