一种求解二次模型信赖域子问题的新算法  

A new algorithm for solving trust-region subproblems with quadratic model

作　　者：朱帅[1] 李亮[1,2] 王希云[2] 张雅琦[2] 于海波[2] 

机构地区：[1]山西大同大学工学院,山西大同037003 [2]太原科技大学应用科学学院,山西太原030024

出　　处：《西南民族大学学报（自然科学版）》2014年第1期91-96,共6页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：山西省自然科学基金(2008011013)

摘　　要：在Hessian矩阵正定的前提下,首先根据信赖域子问题精确求解方法的思想,得到了最优曲线的参数方程,进而建立了一种最优曲线的微分方程模型.针对此微分方程模型,运用中点公式构造了一条折线.从而用该折线代替最优曲线,提出了一种求解二次模型信赖域子问题的新算法.数值结果表明新算法比切线单折线法具有明显的优势.On the premise that Hessian matrix is positive definite, first a parametric equation of the optimal curve is obtained according to the thought of the accurate method for solving trust-region subproblems. Then the paper establishes a differential equation model and constructs a broken line by midpoint formula. Meanwhile, a newt algorithm is presented by using the broken line instead of the optimal curve for solving trust-region subproblems. Numerical results indicate that the new algorithm has obvious advantage over the tangent single dogleg method.

关 键 词：最优曲线 中点公式 微分方程模型 信赖域子问题 

分 类 号：O224[理学—运筹学与控制论]