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An inexact interior point proximal method for the variational inequality problem. (English) Zbl 1169.65063

An inexact interior point proximal method is developed for solving variational inequality problems with maximal monotone operators and linear constraints. The generalized proximal methods used for solving this kind of constrained convex optimization problems make the assumption that the feasible region has nonempty interior. The “extragradient algorithm” developed in this work is also applicable for problems whose feasible region may have empty interior. A full convergence analysis of the algorithm is performed. A numerical implementation of the algorithm is not presented.

MSC:

65K10 Numerical optimization and variational techniques
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J40 Variational inequalities
49J52 Nonsmooth analysis
49J53 Set-valued and variational analysis
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