Research On Algorithm For Solving Trust Region Subproblem Of Quadratic Model

Nonlinear optimization theory,an important branch of operational research,has attracted extensive attention in many fields.The trust region algorithm is a very effective method for solving nonlinear optimization problems,especially unconstrained optimization problems.The key to realize this algorithm is to construct and solve its sub-problems.The most commonly used sub-problem model is the quadratic model.The polyline method is the most classical method for solving the quadratic model.This paper is mainly based on the differential equation model,on the basis of the algorithm proposed by wang xiyun and yu haibo,further studies the higher-order algorithm,and continues to extend the existing conclusions.The first part: introduction,mainly introduces the research status and hot spots of the broken line method for solving the trust region subproblem of the quadratic model,and finally introduces the main work of this paper.In the second and third parts,under the premise of positive definite matrix,two different broken lines are constructed by using the high-order method kutta third-order and Gill's method respectively,and the optimal curve is approximately replaced to solve the sub-problem of the trust region of the quadratic model.Then,the numerical results and feasibility analysis are given through programming.