结合有效集和多维滤子技术的拟Newton信赖域算法(英文)

针对界约束优化问题,提出一个修正的多维滤子信赖域算法.将滤子技术引入到拟Newton信赖域方法,在每步迭代,Cauchy点用于预测有效集,此时试探步借助于求解一个较小规模的信赖域子问题获得.在一定条件下,本文所提出的修正算法对于凸约束优化问题全局收敛.数值试验验证了新算法的实际运行结果.

A Quasi-Newton Trust Region Method Based on the Multidimensional Filter and Active Set Strategy

In this paper,we present a modified filter trust region method for bound constrained problems.We employ the multidimensional filter technique into the quasi-Newton trust region method.The determination of the trial step relies on solving a lower dimensional trust region subproblem as the generalized Cauchy point has been used to predict the active set.Global convergence is promoted through the use of the filter and the convergence theory holds for convex constrained problems.Numerical results demonstrate.the efficiency of the modified algorithm.