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A smoothing Newton-type method for generalized nonlinear complementarity problem
Authors:Xinzhen Zhang  Hefeng Jiang  Yiju Wang
Institution:1. Department of Mathematics, Qufu Normal University, Qufu, Shandong 273165, China;2. Department of Mathematics, Taiyuan Teacher''s College, Taiyuan, Shanxi 030012, China;3. School of Operations Research and Management Sciences, Qufu Normal University, Rizhao Shandong 276800, China;4. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong
Abstract:By using a new type of smoothing function, we first reformulate the generalized nonlinear complementarity problem over a polyhedral cone as a smoothing system of equations, and then develop a smoothing Newton-type method for solving it. For the proposed method, we obtain its global convergence under milder conditions, and we further establish its local superlinear (quadratic) convergence rate under the BD-regular assumption. Preliminary numerical experiments are also reported in this paper.
Keywords:90C33
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