Trust Region Sub-problem Based On Differential Equation Model Research On The R-K Algorithm

Trust-domain method is a kind of computing method of the problem of nonlinear optimization.The research contents include the structure of the trust region model and the solution of the corresponding sub-problems,and the common model is the secondary model.The fold line method is a more efficient and faster algorithm for the correlation algorithm of the quadratic model.With the deepening of the study of the fold line method,a class of algorithms based on the model of the differential equation has obtained a good numerical result through the numerical experiment,which opens up a new kind of calculation way for solving the problem of the trust region.Based on the differential equation model,the class-based algorithm for solving the problem of the trust region is improved,and a class of improved class algorithms for solving the problem of the trust region are proposed.The contents are as follows:In the first chapter,the background and the research status of the trust region algorithm and the sub-problems are introduced,and the work done in this paper is summarized.In the second chapter,based on the variable step size Hun algorithm,the conditions of the theorem are improved,the step size in the algorithm is simplified,an improved variable step size grace algorithm for solving trust region subproblems is proposed,and the well-posedness of the new algorithm is analyzed.the numerical experimental results show that the new algorithm has the advantages of less iterations and fast calculation speed.In the third chapter,based on Hun's third-order algorithm,the conditions of the theorem are improved,the step size of the algorithm is simplified,an improved Hun third-order algorithm for solving trust region subproblems is proposed,and the well-posedness of the new algorithm is analyzed.the numerical experimental results show that the new algorithm has the advantages of less iterations and fast calculation speed.In chapter 4,based on the classical fourth-order algorithm,the conditions of the theorem are improved,the specific step size of the algorithm is given,an improved classical fourth-order algorithm for solving trust region subproblems is proposed,and the well-posedness of the new algorithm is analyzed.the numerical experimental results show that the new algorithm has the advantages of less iterations and fast calculation speed.