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 B_k.The convergence properties of the algorithm are established.Finally,detailed numerical results are reported to show that our algorithm is efficient.
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