Lagrangian Globalization Methods for Nonlinear Complementarity Problems 1 Xiaojun Chen 2 Department of Mathematics and Computer Science Shimane University Matsue 690-8504, Japan E-mail: chen@math.shimane-u.ac.jp Liqun Qi School of Mathematics The University of New South Wales Sydney, New South Wales 2052, Australia E-mail: L.Qi@unsw.edu.au Yufei Yang 3 Department of Applied Mathematics Hunan University Changsha, Hunan 410082, China October 29, 1999 Abstract This paper extends the Lagrangian globalization (LG) method to the nons- mooth equation Φ(x) = 0 arising from nonlinear complementarity problems NCP and presents a descent algorithm for the LG phase. The aim of this paper is not to present a new method for solving NCP, but to find ˆ x such that ‖Φ(ˆ x)‖ < ‖Φ(¯ x)‖ when the NCP has a solution and ¯ x is a stationary point but not a solution. Key Words: Nonlinear complementarity problem, global convergence, Lagrangian. AMS Subject Classification. 90C30, 65K10 1 This work is supported by the Australian Research Council. 2 The work of this author is partly supported by the Scientific Research Grant C11640119 from the Japanese Ministry of Education. 3 Present address: School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia, E-mail: yang@maths.unsw.edu.au