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A Smooth Newton Method For Solving Nonlinear Complementarity Problems

Posted on:2011-08-11Degree:MasterType:Thesis
Country:ChinaCandidate:X X BaiFull Text:PDF
GTID:2120360305991351Subject:Operational Research and Cybernetics
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In this dissertation, a smooth damped Newton method for solving the nonlinear comple-mentarity problem NCP(F) is presented by reformulating NCP(F) to a system of smooth equa-tions. The algorithm is proved to be globally convergent under the assumption that F is P0+R0 function. However, the local superlinear convergence is not guaranteed since the Jacobian ma-trix of the system of smooth equations at the solution is a zero matrix. To overcome this defect, a perturbation strategy is given by which an iterative point xk can be perturbed to xk which belong to the star-like region presented in A. O. Griewank[38] and Ren Yufang[53],it can be proved that the sequence generated by the smooth Newton iteration with unit step size starting from xk is quickly linearly convergent to an approximate solution of NCP(F). Numerical re-sults show that, starting from any initial point x0∈Rn, the sequence {xk} generated by the smooth damped Newton method is quickly convergent to near the solution, and starting from the perturbation point xk the sequence generated by the smooth Newton iteration with unit step size is quickly convergent to an approximate solution. Compared with the existing non-smooth or smoothing Newton methods, the smooth Newton method presented in this dissertation is simple and easy to the practical applications.
Keywords/Search Tags:Nonlinear complementarity problem, Linear convergence, Smooth Newton method, Singular points
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