On the Resolution of the Generalized Nonlinear Complementarity Problem

Minimization of a differentiable function subject to box constraints is proposed as a strategy to solve the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone. It is not necessary to solve nontrivial subproblems nor to calculate projections that complicate and sometimes even disable the implementation of algorithms for solving these kind of problems. Theoretical results that relate stationary points of the function that is minimized to the solutions of the GNCP are presented. Perturbations of the GNCP are also considered and results are obtained that allow the resolution of GNCP's with very general assumptions on the data. These theoretical results support the conjecture that local methods for box constrained optimization applied to the associated problem are efficient tools for solving the GNCP. Numerical experiments are presented that encourage the use of this approach.