Superlinear Convergence of an Interior-Point Method for Monotone Variational Inequalities

We describe an infeasible-interior-point algorithm for monotone variational inequality problems and prove that it converges globally and superlinearly under standard conditions plus a constant rank constraint qualification. The latter condition represents a generalization of the two types of assumptions made in existing superlinear analyses; namely, linearity of the constraints and linear independence of the active constraint gradients. 1 Introduction We consider the monotone variational inequality over a closed convex set C ae IR N : Find z 2 C such that (z 0 \Gamma z) T \Phi(z) 0; for all z 0 2 C. (1) The mapping \Phi : IR N ! IR N is assumed to be continuously differentiable (C 1 ) and monotone; the latter property means that (z 0 \Gamma z) T (\Phi(z 0 ) \Gamma \Phi(z)) 0 for all z 0 ; z 2 IR N . We assume that C is defined as an intersection of finitely many algebraic inequalities; that is, C = fz 2 IR N j g(z) 0g; (2) where g : IR N ! IR P is a C..