Computer Engineering and Applications ›› 2018, Vol. 54 ›› Issue (6): 55-61.DOI: 10.3778/j.issn.1002-8331.1707-0457

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Heun third-order algorithm for solving indefinite trust region subproblems

DONG Jianxin1, LI Linjun2, WANG Xiyun2   

  1. 1.Department of Mathematics, Changzhi University, Changzhi, Shanxi 046011, China
    2.School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China
  • Online:2018-03-15 Published:2018-04-03

解不定信赖域子问题的Heun三阶算法

董建新1,李琳俊2,王希云2   

  1. 1.长治学院 数学系,山西 长治 046011
    2.太原科技大学 应用科学学院,太原 030024

Abstract: For the trust region subproblems, it is modified by Bunch-Parlett method when the Hessian matrix is indefinite. In addition, symmetric positive-definite matrix is also constructed, and the stator problem is transformed into a positive-definite subproblem. The Heun third-order algorithm is given by using a new polygonal line to approximate the solution curve. Then, the feasibility of this algorithm is theoretically proved by analyzing the properties of path of Heun third-order polyline. Finally, the numerical experiments of two test-function show that the algorithm is effective.

Key words: trust region subproblems, differential equation model, indefinite matrix, Heun third-order algorithm

摘要: 针对信赖域子问题,当Hessian矩阵不正定时,利用Bunch-Parlett法对矩阵进行修正,构造了对称正定的矩阵,将不定子问题转化为正定子问题,用新的折线来逼近最优解曲线,给出了求解的Heun三阶算法。通过对Heun三阶折线路径性质的分析,理论上证明了算法的适定性。利用两个测试函数进行了数值实验,结果表明该算法有效。

关键词: 信赖域子问题, 微分方程模型, 不定矩阵, Heun三阶算法