Trust-region method for box-constrained semismooth equations and its applications to complementary problems

Abstract

In this paper, we propose a new trust-region algorithm for bound-constrained semismooth systems of equations. Trust-region subproblem is defined by minimizing a quadratic function subject only to a rectangular constraint. By employing a new active set and nonmonotone techniques, solution of the equations can be found effective. Global and local convergence results of the proposed algorithm are established under reasonable conditions. The algorithm is applied and tested on complementary problems and the experiments show that our method is efficient.