解不定信赖域子问题的Heun三阶算法  

Heun third-order algorithm for solving indefinite trust region subproblems

作　　者：董建新[1] 李琳俊 王希云[2] 

机构地区：[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

出　　处：《计算机工程与应用》2018年第6期55-61,共7页Computer Engineering and Applications

基　　金：国家自然科学基金青年项目(No.61602061);山西省"131"领军人才工程项目;长治学院校级科研项目(No.201607)

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。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 positivedefinite 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 thirdorder polyline. Finally, the numerical experiments of two test-function show that the algorithm is effective.

关 键 词：信赖域子问题 微分方程模型 不定矩阵 Heun三阶算法 

分 类 号：O221[理学—运筹学与控制论]