A modified Newton method for solving variational inequalities
Patrice Marcotte, Jean‐Pierre Dussault · 1985
In this paper we show how the basic Newton method for solving variational inequalities can be modified to yield an algorithm that monotonically decreases the gap function associated with the variational inequality, by solving a sequence of linear programs. Convergence of the algorithm does not depend on strict monotonicity assumptions. However, under strict complementarity and strong monotonicity assumptions, quadratic convergence is achieved.