A Nonsmooth L-M Method for Solving the Generalized Nonlinear Complementarity Problem over a Polyhedral Cone

• DOI: 10.1007/s00245-005-0823-4
• Publication Date: 2005-05-11T08:34:45Z
• Authors: Yiju Wang; Fengming Ma; Jianzhong Zhang
• Keywords: Nonlinear complementarity problem; Cone (formal languages); Complementarity (molecular biology); Stationary point

In this paper the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone is reformulated as a system of nonsmooth equations. Based on this reformulation, the famous Levenberg-Marquardt (L-M) algorithm is employed to obtain its solution. Theoretical results that relate the stationary points of the merit function to the solution of the GNCP are presented. Under mild assumptions, we show that the L-M algorithm is both globally and superlinearly convergent. Moreover, a method to calculate a generalized Jacobian is given and numerical experimental results are presented.