求解信赖域子问题的Newton-GMRES方法

摘要：

为求解信赖域子问题，通过构造新的光滑函数将子问题的互补模型转化成等价的方程组，将非精确牛顿法与GMRES算法相结合，得到求解信赖域子问题的NewtonGMRES算法，在一定条件下证明该算法的全局收敛性与适定性。数值实验结果表明，该算法可行有效。

关键词：

信赖域子问题；非精确牛顿法；光滑函数；全局收敛

中图分类号：O221.2

文献标志码：A

NewtonGMRES  Method for Solving Trust Region Subproblems

YIN Wanru， RUI Shaoping

（School of Mathematical Sciences， Huaibei Normal University， Huaibei 235000， China）

Abstract：

In order to solve the trust region subproblem NewtonGMRES algorithm  was constructed with a new smooth approximation function， complementary model of subproblem was converted into an equivalent system of equations. The inexact Newton method was combined with the GMRES algorithm to obtain the NewtonGMRES algorithm for solving trust region subproblems. The convergence and wellposedness of the algorithm was proved under certain conditions. Numerical experimental results show that the algorithm is practicable and effective.

Keywords：

trust region subproblem; inexact Newton method; smooth function; global convergence

针对无约束优化问题

minx∈Rnfx（1）

其中，f：Rn→R是二次连续可微函数，信赖域算法具有较强的收敛性，是解决无约束优化问题的重要算法，实现的关键步骤就是子问题的求解。（剩余7421字）