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One-step smoothing Newton method for solving the mixed complementarity problem with a function
Authors:Jia Tang   Sanyang Liu  Changfeng Ma
Affiliation:aDepartment of Mathematics and Computing Science, Xidian University, Xi’an 710071, PR China;bSchool of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, PR China
Abstract:The mixed complementarity problem (denote by MCP(F)) can be reformulated as the solution of a smooth system of equations. In the paper, based on a perturbed mid function, we propose a new smoothing function, which has an important property, not satisfied by many other smoothing function. The existence and continuity of a smooth path for solving the mixed complementarity problem with a P0 function are discussed. Then we presented a one-step smoothing Newton algorithm to solve the MCP with a P0 function. The global convergence of the proposed algorithm is verified under mild conditions. And by using the smooth and semismooth technique, the rate of convergence of the method is proved under some suitable assumptions.
Keywords:Mixed complementarity problem   Smoothing function   Boundedness of iteration sequence   One-step smoothing Newton method   Global convergence   The rate of convergence
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