| 解非凸半定规划的一个Lagrange方法 |
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| 引用本文： | 李敬玉,田志远,张甲. 解非凸半定规划的一个Lagrange方法[J]. 青岛大学学报(自然科学版), 2011, 24(1): 10-14. DOI: 10.3969/j.issn.1006-1037.2011.01.003 |
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| 作者姓名： | 李敬玉 田志远 张甲 |
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| 作者单位： | 青岛大学数学科学学院,山东,青岛,266071 |
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| 摘 要： | 基于一个求解一般非凸半定规划问题的非线性Lagrange函数，给出了其相关算法，研究了函数的性质，证明了算法的收敛性。在适当的条件下，当罚参数大于某一阈值时，算法产生的序列局部收敛，由此给出了与罚参数相关的解的误差估计。
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| 关 键 词： | 非凸半定规划 非线性Lagrange函数 收敛性 |
A Lagrange Method for Nonconvex Semidefinite Optimization |
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| LI Jing-yu,TIAN Zhi-yuan,ZHANG Jia. A Lagrange Method for Nonconvex Semidefinite Optimization[J]. Journal of Qingdao University(Natural Science Edition), 2011, 24(1): 10-14. DOI: 10.3969/j.issn.1006-1037.2011.01.003 |
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| Authors: | LI Jing-yu TIAN Zhi-yuan ZHANG Jia |
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| Affiliation: | LI Jing-yu,TIAN Zhi-yuan,ZHANG Jia(College of Mathematics,Qingdao University,Qingdao 266071,China) |
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| Abstract: | A nonlinear Lagrange function for solving nonconvex semidefinite programming is proposed.Its related algorithm and properties are studied.And the convergence of the algorithm is proved.It is proved that the sequence generated by Lagrangian is locally convergent.When the penalty parameter is larger than a threshold under a set of suitable conditions.There by the error estimate of the solution is obtained which depends on the penalty parameter. |
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| Keywords: | nonconvex semidefinite programming nonlinear Lagrange function convergence |
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