Homogeneous analytic center cutting plane methods for convex problems and variational inequalities

In this paper we consider a new analytic center cutting plane method in an extended space. We prove the efficiency estimates for the general scheme an d show that these results can be used in the analysis of a feasibility prob lem, the variational inequality problem, and the problem of constrained min imization. Our analysis is valid even for problems whose solution belongs t o the boundary of the domain.