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| 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. |
| 关键词: 矩阵迹极小化 Gramian表示 非线性共轭梯度法 |
| DOI： |
| 分类号:0241.6 |
| 基金项目: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）. |
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| THE NONLINEAR CONJUGATE GRADIENT METHOD FOR SOLVING A CLASS OF THE MATRIX TRACE MINIMIZATION PROBLEM |
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LI Chun-mei,WANG Cui-fang,DUAN Xue-feng
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| Abstract: |
| 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. |
| Key words: matrix trace minimization Gramian representation nonlinear conjugate gradient method |
