A family of merit functions are proposed, which are the generalization of several existing merit functions. A number of favorable properties of the proposed merit functions are established. By using these properties, a merit function method for solving nonlinear complementarity problem is investigated, and the global convergence of the proposed algorithm is proved under some standard assumptions. Some preliminary numerical results are given.

Recently, Hu, Huang and Chen [Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems, J. Comput. Appl. Math. 230 (2009): 69-82] introduced a family of generalized NCP-functions, which include many existing NCP-functions as special cases. They obtained several favorite properties of the functions; and by which, they showed that a derivative-free descent method is globally convergent under suitable assumptions. However, no result on convergent rate of the method was reported. In this paper, we further investigate some properties of this family of generalized NCP-functions. In particular, we show that, under suitable assumptions, the iterative sequence generated by the descent method discussed in their paper converges globally at a linear rate to a solution of the nonlinear complementarity problem. Some preliminary numerical results are reported, which verify the theoretical results obtained.

No abstract

Abstract. Based on a family of generalized merit functions, a merit function method for solving nonlinear complementarity problems was proposed by Lu, Huang and Hu [Properties of a family of merit functions and a merit function method for the NCP, Appl. Math.-J. Chinese Univ., 2010, 25: 379-390], where, the global convergence of the method was proved. However, no the result on the convergence rate of the method was reported. In this short paper, we show that the method proposed in the above paper is globally linearly convergent under suitable assumptions.