An Adaptive Filter Trust Region Method And An SQP Algorithm For Automatic Determining The Condition Of The Filter

The filter method was firstly proposed by Fletcher and Leyffer for solving non-linear programming(NLP),for its excellent numerical results.Nowdays many researchers begin to show interest in it.which made progress quickly in constrained optimization field. Especially,this method has been a research hot spot for non-linear optimization in the recent decade.The software for solving NLP has developed and it's better than other softwares in solving some problems.The thesis researches into the fil-ter method and trust region met hod, and we make some improvement the acceptance conditions of the filter.In chapter one,the author firstly introduces the TR method,filter al-gorithm,the present situation of the research and the work that the thesis has done In chapter two,an adaptive filter trust region method is presented and analyzed. we combine the filter method with the adaptive trust region method,if a trial step is not accepted,we perform a filter method to find a successful iterative point. Under some mild conditions,the global conver-gence results of the new method are proved. Numerical experiments show the numerical results of the new method are efficient.In chapter three, a filter SQP algorithm with line search is presented and analyzed.This algorithm does some improvement into the acceptance conditions of the filter,adopts the acceptance conditions of filter which are automatically determined,and proves the strong global convergence properties.