解无约束优化问题的一个新的非单调信赖域算法

A New Non-monotone Trust Region Algorithm for Solving Unconstrained Optimization Problems

在传统信赖域方法的基础上,提出了求解无约束最优化问题的一个新的带非单调线搜索的信赖域算法.该算法采用非单调Wolfe线搜索技术获得迭代步长,新算法在每一迭代步只需求解一次信赖域子问题,克服了每次迭代求解信赖域子问题时计算量较大的缺点.在一定条件下,证明了算法的全局收敛性.数值实验结果表明该算法是有效的.

Based on the traditional trust region method, a new trust region algorithm with non-monotone line search is proposed for solving unconstrained optimization problems. The stepsize is obtained making use of non-monotone Wolfe line search rule. The new algorithm solves the trust region subproblem only once at each iteration, which overcomes the short- comings of large amount of calculation when solving the subproblem at each iteration. The global convergence of the algorithm are proved under certain conditions. Some numerical re- sults are reported, which shows that the algorithm is quite effective.