North-Holland A general descent framework for the monotone variational inequality problem

We present a framework for descent algorithms that solve the monotone variational inequality problem VIPv which consists in finding a solution v * ~ satisfying s(v*)T(v- v*)>1 O, for all ve~2 ~ 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, we show that a variant of the descent method where ach subproblem is only solved approximately is globally convergent under certain conditions. Key words: Variational inequalities, descent methods, optimization. 1