一种求解信赖域子问题的多割线折线算法  

A multi-secant dogleg algorithm for solving trust-region subproblems

作　　者：李亮[1] LI Liang(Xixian Senior High School Affiliated to Central China Normal University,Xixian Henan 464300)

机构地区：[1]华中师范大学附属息县高级中学,河南息县464300

出　　处：《宁夏师范学院学报》2022年第1期24-29,共6页Journal of Ningxia Normal University

摘　　要：在Hessian矩阵正定的情况下,利用线性插值方法构造一条多割线折线,证明了多割线折线路径的合理性,并提出了一种求解信赖域子问题的多割线折线算法.通过与切线单折线和分段切线算法的数值实验做比较,表明新算法是有效且可行的.On the premise that Hessian matrix is a positive definite matrix,a multi-secant dogleg is constructed by using the linear interpolation.And the rationality of the multi-secant dogleg path is demonstrated.Then a multi-secant dogleg algorithm for solving trust-region subproblems is presented.Through the comparison with tangent single dogleg method and subsection tangent algorithm,the results of numerical experiments indicate that this algorithm is effective and practical.

关 键 词：线性插值 多割线折线算法 非线性方程 信赖域子问题 

分 类 号：O221[理学—运筹学与控制论]