A NEWTON-TYPE METHOD FOR POSITIVE-SEMIDEFINITE LINEAR COMPLEMENTARITY-PROBLEMS

The paper presents a damped and perturbed Newton-type method for solving linear complementarity problems with positive-semidefinite matrices M. In particular, the following properties hold: all occurring subproblems are linear equations; each subproblem is uniquely solvable without any assumption; every accumulation point generated by the method solves the linear complementarity problem. The additional property of M to be an R(o)-matrix is sufficient, but not necessary, for the boundedness of the iterates. Provided that M is positive definite on a certain subspace, the method converges Q-quadratically.