A Non-Monotomic Trust Region Algorithm With Line Search Based On The Conic Model

Traditional trust region methods are based on a quadratic model, it is an important class of numerical calculation methods, because of its strong adaptability and convergence of optimization algorithms. But for strong non-quadratic form and the sharp change in curvature function, the methods based on a quadratic model are not good. In recent years, the conic model for the study of trust region algorithm has aroused wide spread concern, made up for the deficiencies of quadratic model trust region algorithm. This thesis combines the non-monotone technique and proposes a non-monotonic conic model trust region algorithm with line search.There are four chapters in this paper. In chapter one, we firstly introduce the basic idea of the trust region algorithm. Then, we give the properties of a conic model and overview about the present situation of conic model. In chapter two, by means of the dogleg algorithm for solving the sub-problem, a non-monotonic conic model with line search algorithm is introduced, which is the development of the quadratic model trust region algorithm and traditional conic model of trust region algorithm. Compared with them, the new method has a good numerical result. And the global convergence is proved. In chapter three, for some unreasonable factors existed in accept conditions of conic model trust region algorithm, we proposed an improved non-monotonic trust region algorithm, and remains the characteristic of convergence. In chapter four, a new non-monotone BFGS-trust-region algorithm based on conic model is proposed by combining the BFGS update, and the global convergence are proved under finite supposed conditions.