中文摘要：

本文考虑求解大规模无约束最优化问题 minf（x）,x∈R^n,其中f：R^n→R是二阶连续可微的实值目标函数,n是一个比较大的正整数.在求解问题（1.1）时,通常的迭代法产生一个迭代点列x0,x1,x2,…,

英文摘要：

A new method combining trust region and second order line search for large scale unconstrained optimization is presented in this paper.The trust region subproblem is solved inexactly,and the solution only satisfies the Cauchy descent condition which may not satisfy the gradient-related sufficient descent condition.A second order line search technique is employed for dealing with this problem,and the step length of the second order line search is bounded above and below away from zero.The new method with average non-monotone technique is proposed,and its convergence is proved.Preliminary numerical results on a set of large scale CUTEr test problems are reported.These results show the efficiency and prominence of the algorithm.