文章结合非单调信赖域方法和非单调线搜索技术提出了一类新的无约束优化算法.与传统的非单调信赖与算法相比,此算法在每步都采用非单调Wolfe线搜索得到下一个迭代点,信赖域半径由子问题的近似解和线搜索的步长调节, 这样得到的新算法不仅不需重解子问题,而且在每步迭代保证目标函数的近似海赛矩阵的正定性, 在一定条件下证明了算法具有全局收敛性和$Q$-二次收敛性.数值试验表明算法是十分有效的.

In this paper, we present a nonmonotonic trust region algorithm with nonmonotonic line search. Unlike traditional nonmonotonic trust region algorithms, the next point is given by the nonmonotonic Wolfe line search at each iteration, and trust region radius is adjusted by subproblem approximate solution and line
search step length. The new algorithm not only does not need to re-solve sub-problems, but also maintains a positive definite approximation to the Hessian of the objective function. We prove the global convergence and $Q$-quadratic convergence of the algorithm. The numerical results show the effectiveness of the algorithm.