Computational & Applied Mathematics
On-line version ISSN 1807-0302
BURACHIK, Regina S.; LOPES, Jurandir O. and DA SILVA, Geci J.P.. An inexact interior point proximal method for the variational inequality problem. Comput. Appl. Math. [online]. 2009, vol.28, n.1, pp. 15-36. ISSN 1807-0302. http://dx.doi.org/10.1590/S0101-82052009000100002.
We propose an infeasible interior proximal method for solving variational inequality problems with maximal monotone operators and linear constraints. The interior proximal method proposed by Auslender, Teboulle and Ben-Tiba  is a proximal method using a distance-like barrier function and it has a global convergence property under mild assumptions. However, this method is applicable only to problems whose feasible region has nonempty interior. The algorithm we propose is applicable to problems whose feasible region may have empty interior. Moreover, a new kind of inexact scheme is used. We present a full convergence analysis for our algorithm.
Keywords : maximal monotone operators; outer approximation algorithm; interior point method; global convergence.