Self-adaptive Trust Region Methods For System Of Nonlinear Equations

In the dissertation, we consider the self-adaptive trust region method for system of nonlinear equations, and apply this method to solve generalized nonlinear complementarity problems. When we consider the system of generalized nonlinear complementarity problems, we first reformulate the generalized nonliner complementarity problem into a nonlinear equations problem, and then we apply the self-adaptive trust region method to solve it. Three chapters are included in this dissertation.In chapter 1, we prensent the introduction, which mainly describes the research value and research situations of nonlinear equations and generalized non-liner complementarity problems. Furthermore, the main task is also presented briefly.In chapter 2, we propose a self-adaptive trust region method for system of nonlinear equations. The superiority of the self-adaptive trust region method comparing with traditional trust region method is that the trust region radius in self-adaptive trust region method can be adjusted by itself according to the information of the current iterate informations. In this thesis, we give a suitable trust region radius and we design a self-adaptive trust region method and we prove that the method has global convergence and Q-second convergence rate under mild conditions. Numerical results show that we choose a suitable initial adaptive trust region radius at each iteration so as to reduce the number of iterations, function and gradient evaluations.In chapter 3, we present a self-adaptive trust region method for solving generalized nonlinear complementarity problems.We first present some equivalent reformulations, and then we apply the self-adaptive trust region method to solve it. In the thesis we combine the LMM mothed and self-adaptive trust region method to obtain search direction (<4,p): when we apply LMM mothed to obtain LMM direction (dj^),deposited number is small and easy to account;when we apply self-adaptive trust region method to account self-adaptive trust region direction (djjTp),we plentyly use the information of the current iterate,in subproblem some parameters could be adjusted by itself ,it is propitious to ameliorate convergence of the method . We adhibit the adjustive parameter Uk = ||//(wfc)||*,