A quadratically convergent long-step interior-point method for nonlinear monotone variational inequality problems

Jie Sun and Gongyun Zhao

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

Technical Report, April, 1996.