A Class Of Nonmonotone Trust Region Methods And Numerical Experiment Research

In this thesis, we consider some topics about the nonmonotone trust region method for unconstrained minimization problems.In Chapter 2, we combine the nonmonotone technique and adaptive technique to form a trust region method. Instead of the monotone sequence, the nonmonotone sequence of function values are employed. With adaptive technique, the trust region radius â–³_k can be adjusted automatically to improve the efficiency of trust region methods. By means of Bunch-Parlett factorization, we construct indefinite dogleg path methods for solving the trust region subproblem which can handle the indefinite approximate Hessian B_k . The resulting indefinite dogleg path algorithms are easy to implement. We prove the convergence properties of these algorithms and analyze its convergence rate. Numerical results are reported to show that our algorithm is efficient.In Chapter 3, we first compare the numerical efficiency of two classes of nonmonotone trust region (NTR) algorithms in which one has upper bound on the trust region radius, and the other has not in the context of unconstrained optimization. For Algorithm NTR2, we examine the sensitivity of the algorithm on the parameters, such as M, which related to the nonmonotone technique and the initial trust region radius â–³₀ . We show that the numerical efficiency of NTR algorithm can be improved by choosing appropriate parameters. On the basis of extensive numerical tests, the superior ranges of these parameters are recommended.