An interior point method for the nonlinear complementarity problem Original Research Article

We present an interior point method for the nonlinear complementarity problem which converges, whenever the problem has solutions, for any paramonotone operator (i.e., monotone and such that 〈F(x)−F(y), x−y〉 = 0 implies F(x) = F(y)). The iterative step consists of easily computable closed formulae, up to a finite search for a real parameter. Convergence of the algorithm results from its reduction to an interior point method for variational inequalities using Bregman functions, whose iterative step requires a similar finite search plus the solution of a nonlinear equation in one real variable. As an intermediate step in the reduction, we simplify the method for variational inequalities, replacing the solution of the nonlinear equation by a second finite search for another real parameter, which is finally replaced by a closed formula in the case of nonlinear complementarity problems.