The New Cone Model Trust Region Algorithm

For the unconstrained optimization problem, the trust region algorithm is an improtant class of numerical calculation method, and the traditional trust region method for solving this problem is based on quadratic models. However, for strongly non-quadratic form and more dramatic change of curvature function, the conic function with approximation of the relative effect of the objective function is better. So the trust region method of conic model attracted wide attention from researchers. Especially, the new trust region algorithm of conic model is proposed and studied in 2005, it broken through the limitations of traditional conic model trust region algorithm for solving the optimal value only one side of the hyperplane.This article mainly studies the algorithm frame's structure and improvement. It is divided into five chapters. In the first chapter, the basic idea and research of the traditional trust region algorithm is introduced. In the second chapter, the theoretical basis of the conic model trust region algorithm is introduced, and the new conic model trust region algorithm for solving the sub-problem is analysised. The third, forth and fifth chapter are the core of this article. In the third chapter, a nonmonotone self-adaptive trust region algorithm with line search based on the new conic model is proposed. And the subproblems are sloved by the dogleg method. The the numerical results of the new conic model are better than the traditional trust region algorithm. Global convergence is proved under certain conditions. In the forth chapter, a filter self-adaptive trust region algorithm of the new conic model is proposed. The two classic large-scale test functions are tested, and get some good numerical results. In the fifth chapter, a multidimensional line seatch filter trust region algorithm of the new conic model is proposed. This may allow a considerable computational saving, and the global convergence of the algorithm is given under certain conditions.