A Smoothing Trust Region Method for NCPs Based on the Smoothing Generalized Fischer-Burmeister Function (Journal of Computational Mathematics, 2018)
Based on a reformulation of the complementarity problem as a system of nonsmooth equations by using the generalized Fischer-Burmeister function, a smoothing trust region algorithm with line search is proposed for solving general (not necessarily monotone) nonlinear complementarity problems. Global convergence and, under a nonsingularity assumption, local Q-superlinear/Q-quadratic convergence of the algorithm are established. In particular, it is proved that a unit step size is always accepted after a finite number of iterations. Numerical results also confirm the good theoretical properties of our approach.
Keywords: Nonlinear complementarity problem; Smoothing method; Trust region method; Global convergence; Local superlinear convergence.