一类新的非单调信赖域算法

A New Family of Nonmonotone Trust Region Algorithm

提出了一类带线性搜索的非单调信赖域算法.算法将非单调Armijo线性搜索技术与信赖域方法相结合,使算法不需重解子问题.而且由于采用了MBFGS校正公式,使矩阵Bk能较好地逼近目标函数的Hesse矩阵并保持正定传递.在较弱的条件下,证明了算法的全局收敛性.数值结果表明算法是有效的.

In this paper,we propose a trust region algorithm with a nonmonotone line search technique.Because of combining the nonmonotone Armijo line search with trust region method,The new algorithm doesn＇t need to resolve the subproblem.We update B_k by MBFGS method,so B_k approximates to the Hesse of the objective function well and keeps its positive definiteness.Under weaker conditions,we prove the global convergence of the algorithm.Some numerical results show that the new nonmonotone trust region algorithm is efficient.