求解一类矩阵迹极小化问题的非线性共轭梯度法  

THE NONLINEAR CONJUGATE GRADIENT METHOD FOR SOLVING A CLASS OF THE MATRIX TRACE MINIMIZATION PROBLEM

作　　者：李春梅 王翠方[2] 段雪峰 LI Chun-mei;WANG Cui-fang;DUAN Xue-feng(School of Mathematical Science,Guizhou Normal University,Guiyang 550001,China;School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550001 [2]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《数学杂志》2020年第3期323-331,共9页Journal of Mathematics

基　　金：国家自然科学基金项目(11561015,11761024);广西科技项目(AD18281024);广西自然科学基金项目(2016GXNSFFA380009,2017GXNSFBA198082,2016XNSFAA380074)。

摘　　要：本文研究了图分割问题中的矩阵迹极小化问题.利用半正定矩阵的Gramian表示,将该问题转化为无约束优化问题,设计了Armijo线搜索下的非线性共轭梯度方法进行求解.数值例子表明新方法是可行的.In this paper,we consider the trace minimization problem in graph partitioning.Using the Gramian representation of the positive semidefinite matrix,the problem can be formulated as the unconstrained optimization problem,then the nonlinear conjugate method with the Armijo line search is used to solve it.Numerical experiments illustrate the feasibility of the new method.

关 键 词：矩阵迹极小化 Gramian表示 非线性共轭梯度法 

分 类 号：O241.6[理学—计算数学]