Abstract :
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.
