解信赖域子问题的多折线算法  

A Multi-polyline Algorithm for Solving Trust Region Sub-problems

作　　者：申理精[1] 郭栋栋 王希云[1] SHEN Li-jing;GUO Dong-dong;WANG Xi-yun(School of Applied Science,Taiyuan University of Science and Technology,Taiyuan 030024,China;Shanxi College of Applied Science and Technology,Taiyuan 030024,China)

机构地区：[1]太原科技大学应科学院,太原030024 [2]山西应用科技学院,太原030024

出　　处：《太原科技大学学报》2022年第1期61-65,共5页Journal of Taiyuan University of Science and Technology

基　　金：国家自然科学基金(11901421);山西省科技厅青年基金(201901D211285);山西省教育厅教改项目(2018129);太原科技大学校教改项目(202020)。

摘　　要：Hessian阵正定时,基于双割线折线法构造了一条多折线路径来代替最优曲线求解信赖域子问题,形成多折线算法。从几何上分析了多折线算法比割线法求解子问题时更精确,给出了多折线算法的收敛性分析,数值试验与双割线折线法比较知新构造的算法更好。When the Hessian matrix is positive definite,a multi-polyline path based on the double secant polyline method is constructed to solve the trust region sub-problem instead of the optimal curve,and the multi-polyline algorithm is formed.The multi-polyline algorithm is analyzed geometrically to be more accurate than secant method in solving sub-problems,and the convergence analysis of the multi-polyline algorithm is given.Numerical tests show that the new algorithm is better than the double secant polyline method.

关 键 词：信赖域子问题 多折线算法 收敛性 数值试验 

分 类 号：O221[理学—运筹学与控制论]