东北数学（英文版）
東北數學（英文版）
동북수학（영문판）
NORTHEASTERN MATHEMATICAL JOURNAL
2008年
1期
19-30
,共12页
nonmonotone trust region method%adaptive method%indefinite dogleg path%unconstrained minimization%global convergence%superlinear convergence
In this paper,we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems.We set a new ratio of the actual descent and predicted descent.Then,instead of the monotone sequence,the nonmonotone sequence of function values are employed.With the adaptive technique,the radius of trust region △k can be adjusted automatically to improve the efficiency of trust region methods.By means of the Bunch-Parlett factorization,we construct a method with indefinite dogleg path for solving the trust region subproblem which can handle the indefinite approximate Hessian Bk.The convergence properties of the algorithm are established.Finally,detailed numerical results are reported to show that our algorithm is efficient.
