Properties of a family of merit functions and a merit function method for the NCP

Abstract

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.

The Linear Convergence of a Merit Function Method for Nonlinear Complementarity Problems

“…Some promising numerical results were also reported. However, no the result on the convergence rate of the method was reported in [15]. In this short paper, we further investigate the method proposed in [15].…”

“…In this short paper, we further investigate the method proposed in [15]. We will show that the method proposed in [15] is globally linearly convergent under suitable assumptions.…”

“…Based on the function defined by (1), a merit function method for the NCP was proposed in [15]. The investigated method is a derivative-free descent method.…”

“…This kind of methods is particularly suitable for problems where the derivatives of F are not available or are extremely expensive to compute. Based on the analysis on properties of the function defined by (1), the authors in [15] showed that the proposed method is globally convergent under suitable assumptions. Some promising numerical results were also reported.…”

“…In Section 2, we recall some basic concepts, the investigated algorithm and the related results. In Section 3, we establish the linear rate of convergence for the method proposed in [15]. Some final remarks are given in Section 4.…”