Quadratic convergence of a long-step interior-point method for nonlinear monotone variational inequality problems

Abstract

This paper offers an analysis on a standard long-step primaldual interior-point method for nonlinear monotone variational inequality problems. The method has polynomial-time complexity and its q-order of convergence is two. The results are proved under mild assumptions. In particular, new conditions on the invariance of the rank and range space of certain matrices are employed, rather than restrictive assumptions like nondegeneracy.