一种求解二次模型信赖域子问题的休恩算法  

A Heun's Algorithm for Solving Trust-region Subproblems with Quadratic Model

作　　者：李亮[1] 王希云[1] 张雅琦[1] 于海波[1] 

机构地区：[1]太原科技大学应用科学学院,太原030024

出　　处：《太原科技大学学报》2014年第2期151-156,共6页Journal of Taiyuan University of Science and Technology

基　　金：山西省自然科学基金(2008011013);2013山西省高校"131"项目

摘　　要：在Hessian矩阵正定的前提下,首先根据二次模型赖域子问题的精确求解方法的思想,得到了最优曲线的参数方程,进而根据参数方程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,运用求解微分方程的休恩方法构造了一条折线,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休恩算法。通过与切线单折线法的数值实验作比较,数值结果表明新算法比切线单折线法具有明显的优势。In the premise of Hessian matrix as a positive definite matrix,a parametric equation of the optimal curve is obtained according to the thought of the accurate method for solving trust-region subproblems with quadratic mod-el. Then a differential equation model is established,and a broken line is constructed by Heun′s method according to the differential equation model. Meanwhile,a Heun′s algorithm for solving trust-region subproblems with quadratic＆amp;nbsp;model is presented by using the broken line instead of the optimal curve. Through the comparison with the tangent single dogleg method,the results of numerical experiments indicate that the new algorithm has obvious advantage o-ver the tangent single dogleg method.

关 键 词：最优曲线 休恩算法 微分方程模型 信赖域子问题 

分 类 号：O221[理学—运筹学与控制论]